diff --git a/toolchain/check/call.cpp b/toolchain/check/call.cpp
index 94853016a248..0a6ac94cf648 100644
--- a/toolchain/check/call.cpp
+++ b/toolchain/check/call.cpp
@@ -300,6 +300,9 @@ auto PerformCall(Context& context, SemIR::LocId loc_id, SemIR::InstId callee_id,
     return SemIR::ErrorInst::InstId;
   }
   if (callee_function.cpp_overload_set_id.has_value()) {
+    auto self_id = callee_function.self_id;
+    // TODO: Pass self_id into overload resolution so that it's taken into
+    // account when selecting the overload.
     auto resolved_fn_id = PerformCppOverloadResolution(
         context, loc_id, callee_function.cpp_overload_set_id, arg_ids);
     if (!resolved_fn_id) {
@@ -311,6 +314,10 @@ auto PerformCall(Context& context, SemIR::LocId loc_id, SemIR::InstId callee_id,
       return SemIR::ErrorInst::InstId;
     }
     CARBON_CHECK(!callee_function.cpp_overload_set_id.has_value());
+
+    // Preserve the `self` argument from the original callee.
+    CARBON_CHECK(!callee_function.self_id.has_value());
+    callee_function.self_id = self_id;
   }
   if (callee_function.function_id.has_value()) {
     return PerformCallToFunction(context, loc_id, callee_id, callee_function,
diff --git a/toolchain/check/member_access.cpp b/toolchain/check/member_access.cpp
index 0751bb5ec551..d33586e59207 100644
--- a/toolchain/check/member_access.cpp
+++ b/toolchain/check/member_access.cpp
@@ -45,14 +45,34 @@ static auto GetClassElementIndex(Context& context, SemIR::InstId element_id)
   CARBON_FATAL("Unexpected value {0} in class element name", element_inst);
 }
 
-// Returns whether `function_id` is an instance method, that is, whether it has
-// an implicit `self` parameter.
+// Returns whether `function_id` is an instance method: in other words, whether
+// it has an implicit `self` parameter.
 static auto IsInstanceMethod(const SemIR::File& sem_ir,
                              SemIR::FunctionId function_id) -> bool {
   const auto& function = sem_ir.functions().Get(function_id);
   return function.self_param_id.has_value();
 }
 
+// Returns whether the callee function is an instance method, either because
+// it's a Carbon instance method or because it's a C++ overload set that might
+// contain an instance method.
+static auto IsInstanceMethod(const SemIR::File& sem_ir,
+                             const SemIR::CalleeFunction& callee) -> bool {
+  if (callee.function_id.has_value()) {
+    return IsInstanceMethod(sem_ir, callee.function_id);
+  }
+  if (callee.cpp_overload_set_id.has_value()) {
+    // For now, treat all C++ overload sets as potentially containing instance
+    // methods. Overload resolution will handle the case where we actually
+    // found a static method.
+    // TODO: Consider returning `false` if there are no non-instance methods in
+    // the overload set. This would cause us to reject
+    // `instance.(Class.StaticMethod)()` like we do in pure Carbon code.
+    return true;
+  }
+  return false;
+}
+
 // Return whether `type_id`, the type of an associated entity, is for an
 // instance member (currently true only for instance methods).
 static auto IsInstanceType(Context& context, SemIR::TypeId type_id) -> bool {
@@ -372,10 +392,9 @@ static auto PerformInstanceBinding(Context& context, SemIR::LocId loc_id,
                                    SemIR::InstId member_id) -> SemIR::InstId {
   // If the member is a function, check whether it's an instance method.
   if (auto callee = SemIR::GetCalleeFunction(context.sem_ir(), member_id);
-      callee.function_id.has_value()) {
-    if (!IsInstanceMethod(context.sem_ir(), callee.function_id) ||
-        callee.self_id.has_value()) {
-      // Found a static member function or an already-bound method.
+      IsInstanceMethod(context.sem_ir(), callee)) {
+    if (callee.self_id.has_value()) {
+      // Found an already-bound method.
       return member_id;
     }
 
diff --git a/toolchain/check/testdata/interop/cpp/class/access.carbon b/toolchain/check/testdata/interop/cpp/class/access.carbon
index 2aa6bece01ba..b7727162533a 100644
--- a/toolchain/check/testdata/interop/cpp/class/access.carbon
+++ b/toolchain/check/testdata/interop/cpp/class/access.carbon
@@ -161,7 +161,7 @@ struct S {
   auto foo() -> void;
 };
 
-// --- fail_todo_5891_import_function_member_public.carbon
+// --- import_function_member_public.carbon
 
 library "[[@TEST_NAME]]";
 
@@ -169,11 +169,6 @@ import Cpp library "function_member_public.h";
 
 fn F(s: Cpp.S*) {
   //@dump-sem-ir-begin
-  // CHECK:STDERR: fail_todo_5891_import_function_member_public.carbon:[[@LINE+5]]:3: error: missing object argument in method call [MissingObjectInMethodCall]
-  // CHECK:STDERR:   s->foo();
-  // CHECK:STDERR:   ^~~~~~~~
-  // CHECK:STDERR: fail_todo_5891_import_function_member_public.carbon: note: calling function declared here [InCallToFunction]
-  // CHECK:STDERR:
   s->foo();
   //@dump-sem-ir-end
 }
@@ -432,7 +427,7 @@ fn F() {
 // CHECK:STDOUT:   <elided>
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: --- fail_todo_5891_import_function_member_public.carbon
+// CHECK:STDOUT: --- import_function_member_public.carbon
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %S: type = class_type @S [concrete]
@@ -456,10 +451,11 @@ fn F() {
 // CHECK:STDOUT: fn @F(%s.param: %ptr.5c7) {
 // CHECK:STDOUT: !entry:
 // CHECK:STDOUT:   %s.ref: %ptr.5c7 = name_ref s, %s
-// CHECK:STDOUT:   %.loc13: ref %S = deref %s.ref
+// CHECK:STDOUT:   %.loc8: ref %S = deref %s.ref
 // CHECK:STDOUT:   %foo.ref: %.177 = name_ref foo, imports.%.dcb [concrete = constants.%empty_struct]
-// CHECK:STDOUT:   <elided>
-// CHECK:STDOUT:   %S.foo.call: init %empty_tuple.type = call imports.%S.foo.decl(<error>)
+// CHECK:STDOUT:   %bound_method: <bound method> = bound_method %.loc8, %foo.ref
+// CHECK:STDOUT:   %addr: %ptr.5c7 = addr_of %.loc8
+// CHECK:STDOUT:   %S.foo.call: init %empty_tuple.type = call imports.%S.foo.decl(%addr)
 // CHECK:STDOUT:   <elided>
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/interop/cpp/class/base.carbon b/toolchain/check/testdata/interop/cpp/class/base.carbon
index ef4e1b7aa93b..9c66caf8c355 100644
--- a/toolchain/check/testdata/interop/cpp/class/base.carbon
+++ b/toolchain/check/testdata/interop/cpp/class/base.carbon
@@ -10,8 +10,6 @@
 // TIP: To dump output, run:
 // TIP:   bazel run //toolchain/testing:file_test -- --dump_output --file_tests=toolchain/check/testdata/interop/cpp/class/base.carbon
 
-// TODO: Tests marked as `fail_todo_5891_` to fixed as a follow-up of https://github.com/carbon-language/carbon-lang/pull/5891.
-
 // --- derived_to_base_conversion.h
 
 class Base {};
@@ -103,7 +101,7 @@ struct Derived : Base {
   void g() const;
 };
 
-// --- fail_todo_5891_use_base_method.carbon
+// --- use_base_method.carbon
 
 library "[[@TEST_NAME]]";
 
@@ -111,26 +109,12 @@ import Cpp library "base_method.h";
 
 fn CallDirect(d: Cpp.Derived) {
   //@dump-sem-ir-begin
-  // CHECK:STDERR: fail_todo_5891_use_base_method.carbon:[[@LINE+5]]:3: error: missing object argument in method call [MissingObjectInMethodCall]
-  // CHECK:STDERR:   d.f();
-  // CHECK:STDERR:   ^~~~~
-  // CHECK:STDERR: fail_todo_5891_use_base_method.carbon: note: calling function declared here [InCallToFunction]
-  // CHECK:STDERR:
   d.f();
   //@dump-sem-ir-end
 }
 
 fn CallQualified(d: Cpp.Derived) {
   //@dump-sem-ir-begin
-  // CHECK:STDERR: fail_todo_5891_use_base_method.carbon:[[@LINE+9]]:3: error: member name of type `<type of Cpp.g>` in compound member access is not an instance member or an interface member [CompoundMemberAccessDoesNotUseBase]
-  // CHECK:STDERR:   d.(Cpp.Base.g)();
-  // CHECK:STDERR:   ^~~~~~~~~~~~~~
-  // CHECK:STDERR:
-  // CHECK:STDERR: fail_todo_5891_use_base_method.carbon:[[@LINE+5]]:3: error: missing object argument in method call [MissingObjectInMethodCall]
-  // CHECK:STDERR:   d.(Cpp.Base.g)();
-  // CHECK:STDERR:   ^~~~~~~~~~~~~~~~
-  // CHECK:STDERR: fail_todo_5891_use_base_method.carbon: note: calling function declared here [InCallToFunction]
-  // CHECK:STDERR:
   d.(Cpp.Base.g)();
   //@dump-sem-ir-end
 }
@@ -472,7 +456,7 @@ class V {
 // CHECK:STDOUT:   return %Int.as.Copy.impl.Op.call to %return
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: --- fail_todo_5891_use_base_method.carbon
+// CHECK:STDOUT: --- use_base_method.carbon
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %Derived: type = class_type @Derived [concrete]
@@ -517,23 +501,33 @@ class V {
 // CHECK:STDOUT: !entry:
 // CHECK:STDOUT:   %d.ref: %Derived = name_ref d, %d
 // CHECK:STDOUT:   %f.ref: %.5b0 = name_ref f, imports.%.e54 [concrete = constants.%empty_struct.3f3]
-// CHECK:STDOUT:   %addr: %ptr.fb2 = addr_of <error> [concrete = <error>]
-// CHECK:STDOUT:   %.loc13_7.1: %ptr.a97 = as_compatible %addr [concrete = <error>]
-// CHECK:STDOUT:   %.loc13_7.2: %ptr.a97 = converted %addr, %.loc13_7.1 [concrete = <error>]
-// CHECK:STDOUT:   %f__carbon_thunk.call: init %empty_tuple.type = call imports.%f__carbon_thunk.decl(%.loc13_7.2)
+// CHECK:STDOUT:   %bound_method: <bound method> = bound_method %d.ref, %f.ref
+// CHECK:STDOUT:   %.loc8_3.1: ref %Base = class_element_access %d.ref, element0
+// CHECK:STDOUT:   %.loc8_3.2: ref %Base = converted %d.ref, %.loc8_3.1
+// CHECK:STDOUT:   %.loc8_3.3: %Base = bind_value %.loc8_3.2
+// CHECK:STDOUT:   %.loc8_3.4: ref %Base = value_as_ref %.loc8_3.3
+// CHECK:STDOUT:   %addr: %ptr.fb2 = addr_of %.loc8_3.4
+// CHECK:STDOUT:   %.loc8_7.1: %ptr.a97 = as_compatible %addr
+// CHECK:STDOUT:   %.loc8_7.2: %ptr.a97 = converted %addr, %.loc8_7.1
+// CHECK:STDOUT:   %f__carbon_thunk.call: init %empty_tuple.type = call imports.%f__carbon_thunk.decl(%.loc8_7.2)
 // CHECK:STDOUT:   <elided>
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @CallQualified(%d.param: %Derived) {
 // CHECK:STDOUT: !entry:
 // CHECK:STDOUT:   %d.ref: %Derived = name_ref d, %d
-// CHECK:STDOUT:   %Cpp.ref.loc28: <namespace> = name_ref Cpp, imports.%Cpp [concrete = imports.%Cpp]
+// CHECK:STDOUT:   %Cpp.ref.loc14: <namespace> = name_ref Cpp, imports.%Cpp [concrete = imports.%Cpp]
 // CHECK:STDOUT:   %Base.ref: type = name_ref Base, imports.%Base.decl [concrete = constants.%Base]
 // CHECK:STDOUT:   %g.ref: %.7c6 = name_ref g, imports.%.362 [concrete = constants.%empty_struct.49e]
-// CHECK:STDOUT:   %addr: %ptr.fb2 = addr_of <error> [concrete = <error>]
-// CHECK:STDOUT:   %.loc28_18.1: %ptr.a97 = as_compatible %addr [concrete = <error>]
-// CHECK:STDOUT:   %.loc28_18.2: %ptr.a97 = converted %addr, %.loc28_18.1 [concrete = <error>]
-// CHECK:STDOUT:   %g__carbon_thunk.call: init %empty_tuple.type = call imports.%g__carbon_thunk.decl(%.loc28_18.2)
+// CHECK:STDOUT:   %bound_method: <bound method> = bound_method %d.ref, %g.ref
+// CHECK:STDOUT:   %.loc14_3.1: ref %Base = class_element_access %d.ref, element0
+// CHECK:STDOUT:   %.loc14_3.2: ref %Base = converted %d.ref, %.loc14_3.1
+// CHECK:STDOUT:   %.loc14_3.3: %Base = bind_value %.loc14_3.2
+// CHECK:STDOUT:   %.loc14_3.4: ref %Base = value_as_ref %.loc14_3.3
+// CHECK:STDOUT:   %addr: %ptr.fb2 = addr_of %.loc14_3.4
+// CHECK:STDOUT:   %.loc14_18.1: %ptr.a97 = as_compatible %addr
+// CHECK:STDOUT:   %.loc14_18.2: %ptr.a97 = converted %addr, %.loc14_18.1
+// CHECK:STDOUT:   %g__carbon_thunk.call: init %empty_tuple.type = call imports.%g__carbon_thunk.decl(%.loc14_18.2)
 // CHECK:STDOUT:   <elided>
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/interop/cpp/class/method.carbon b/toolchain/check/testdata/interop/cpp/class/method.carbon
index 016ce470f322..bcbd30fe275b 100644
--- a/toolchain/check/testdata/interop/cpp/class/method.carbon
+++ b/toolchain/check/testdata/interop/cpp/class/method.carbon
@@ -11,8 +11,6 @@
 // TIP: To dump output, run:
 // TIP:   bazel run //toolchain/testing:file_test -- --dump_output --file_tests=toolchain/check/testdata/interop/cpp/class/method.carbon
 
-// TODO: Tests marked as `fail_todo_5891_` to fixed as a follow-up of https://github.com/carbon-language/carbon-lang/pull/5891.
-
 // --- object_param_qualifiers.h
 
 struct HasQualifiers {
@@ -27,7 +25,7 @@ struct HasQualifiers {
   void const_ref_ref_this() const&&;
 };
 
-// --- fail_todo_5891_use_object_param_qualifiers.carbon
+// --- use_object_param_qualifiers.carbon
 
 library "[[@TEST_NAME]]";
 
@@ -35,90 +33,60 @@ import Cpp library "object_param_qualifiers.h";
 
 fn F(v: Cpp.HasQualifiers, p: Cpp.HasQualifiers*) {
   //@dump-sem-ir-begin
-  // CHECK:STDERR: fail_todo_5891_use_object_param_qualifiers.carbon:[[@LINE+5]]:3: error: missing object argument in method call [MissingObjectInMethodCall]
-  // CHECK:STDERR:   v.const_this();
-  // CHECK:STDERR:   ^~~~~~~~~~~~~~
-  // CHECK:STDERR: fail_todo_5891_use_object_param_qualifiers.carbon: note: calling function declared here [InCallToFunction]
-  // CHECK:STDERR:
   v.const_this();
-  // CHECK:STDERR: fail_todo_5891_use_object_param_qualifiers.carbon:[[@LINE+5]]:3: error: missing object argument in method call [MissingObjectInMethodCall]
-  // CHECK:STDERR:   v.const_ref_this();
-  // CHECK:STDERR:   ^~~~~~~~~~~~~~~~~~
-  // CHECK:STDERR: fail_todo_5891_use_object_param_qualifiers.carbon: note: calling function declared here [InCallToFunction]
-  // CHECK:STDERR:
   v.const_ref_this();
 
-  // CHECK:STDERR: fail_todo_5891_use_object_param_qualifiers.carbon:[[@LINE+5]]:3: error: missing object argument in method call [MissingObjectInMethodCall]
-  // CHECK:STDERR:   p->plain();
-  // CHECK:STDERR:   ^~~~~~~~~~
-  // CHECK:STDERR: fail_todo_5891_use_object_param_qualifiers.carbon: note: calling function declared here [InCallToFunction]
-  // CHECK:STDERR:
   p->plain();
-  // CHECK:STDERR: fail_todo_5891_use_object_param_qualifiers.carbon:[[@LINE+5]]:3: error: missing object argument in method call [MissingObjectInMethodCall]
-  // CHECK:STDERR:   p->ref_this();
-  // CHECK:STDERR:   ^~~~~~~~~~~~~
-  // CHECK:STDERR: fail_todo_5891_use_object_param_qualifiers.carbon: note: calling function declared here [InCallToFunction]
-  // CHECK:STDERR:
   p->ref_this();
-  // CHECK:STDERR: fail_todo_5891_use_object_param_qualifiers.carbon:[[@LINE+5]]:3: error: missing object argument in method call [MissingObjectInMethodCall]
-  // CHECK:STDERR:   p->const_this();
-  // CHECK:STDERR:   ^~~~~~~~~~~~~~~
-  // CHECK:STDERR: fail_todo_5891_use_object_param_qualifiers.carbon: note: calling function declared here [InCallToFunction]
-  // CHECK:STDERR:
   p->const_this();
-  // CHECK:STDERR: fail_todo_5891_use_object_param_qualifiers.carbon:[[@LINE+5]]:3: error: missing object argument in method call [MissingObjectInMethodCall]
-  // CHECK:STDERR:   p->const_ref_this();
-  // CHECK:STDERR:   ^~~~~~~~~~~~~~~~~~~
-  // CHECK:STDERR: fail_todo_5891_use_object_param_qualifiers.carbon: note: calling function declared here [InCallToFunction]
-  // CHECK:STDERR:
   p->const_ref_this();
   //@dump-sem-ir-end
 }
 
-// --- fail_bad_5891_object_param_qualifiers_by_value.carbon
+// --- fail_bad_object_param_qualifiers_by_value.carbon
 
 library "[[@TEST_NAME]]";
 
 import Cpp library "object_param_qualifiers.h";
 
 fn Value(v: Cpp.HasQualifiers) {
-  // CHECK:STDERR: fail_bad_5891_object_param_qualifiers_by_value.carbon:[[@LINE+5]]:3: error: missing object argument in method call [MissingObjectInMethodCall]
+  // CHECK:STDERR: fail_bad_object_param_qualifiers_by_value.carbon:[[@LINE+5]]:3: error: `addr self` method cannot be invoked on a value [AddrSelfIsNonRef]
   // CHECK:STDERR:   v.plain();
-  // CHECK:STDERR:   ^~~~~~~~~
-  // CHECK:STDERR: fail_bad_5891_object_param_qualifiers_by_value.carbon: note: calling function declared here [InCallToFunction]
+  // CHECK:STDERR:   ^
+  // CHECK:STDERR: fail_bad_object_param_qualifiers_by_value.carbon: note: initializing function parameter [InCallToFunctionParam]
   // CHECK:STDERR:
   v.plain();
 
   // TODO: This should remain invalid once we support `volatile`.
-  // CHECK:STDERR: fail_bad_5891_object_param_qualifiers_by_value.carbon:[[@LINE+7]]:3: error: semantics TODO: `Unsupported: object parameter type: volatile struct HasQualifiers` [SemanticsTodo]
+  // CHECK:STDERR: fail_bad_object_param_qualifiers_by_value.carbon:[[@LINE+7]]:3: error: semantics TODO: `Unsupported: object parameter type: volatile struct HasQualifiers` [SemanticsTodo]
   // CHECK:STDERR:   v.volatile_this();
   // CHECK:STDERR:   ^~~~~~~~~~~~~~~~~
-  // CHECK:STDERR: fail_bad_5891_object_param_qualifiers_by_value.carbon:[[@LINE+4]]:3: note: in call to Cpp function here [InCallToCppFunction]
+  // CHECK:STDERR: fail_bad_object_param_qualifiers_by_value.carbon:[[@LINE+4]]:3: note: in call to Cpp function here [InCallToCppFunction]
   // CHECK:STDERR:   v.volatile_this();
   // CHECK:STDERR:   ^~~~~~~~~~~~~~~~~
   // CHECK:STDERR:
   v.volatile_this();
 
-  // CHECK:STDERR: fail_bad_5891_object_param_qualifiers_by_value.carbon:[[@LINE+5]]:3: error: missing object argument in method call [MissingObjectInMethodCall]
+  // CHECK:STDERR: fail_bad_object_param_qualifiers_by_value.carbon:[[@LINE+5]]:3: error: `addr self` method cannot be invoked on a value [AddrSelfIsNonRef]
   // CHECK:STDERR:   v.ref_this();
-  // CHECK:STDERR:   ^~~~~~~~~~~~
-  // CHECK:STDERR: fail_bad_5891_object_param_qualifiers_by_value.carbon: note: calling function declared here [InCallToFunction]
+  // CHECK:STDERR:   ^
+  // CHECK:STDERR: fail_bad_object_param_qualifiers_by_value.carbon: note: initializing function parameter [InCallToFunctionParam]
   // CHECK:STDERR:
   v.ref_this();
 
-  // CHECK:STDERR: fail_bad_5891_object_param_qualifiers_by_value.carbon:[[@LINE+7]]:3: error: semantics TODO: `Unsupported: object parameter type: struct HasQualifiers &&` [SemanticsTodo]
+  // CHECK:STDERR: fail_bad_object_param_qualifiers_by_value.carbon:[[@LINE+7]]:3: error: semantics TODO: `Unsupported: object parameter type: struct HasQualifiers &&` [SemanticsTodo]
   // CHECK:STDERR:   v.ref_ref_this();
   // CHECK:STDERR:   ^~~~~~~~~~~~~~~~
-  // CHECK:STDERR: fail_bad_5891_object_param_qualifiers_by_value.carbon:[[@LINE+4]]:3: note: in call to Cpp function here [InCallToCppFunction]
+  // CHECK:STDERR: fail_bad_object_param_qualifiers_by_value.carbon:[[@LINE+4]]:3: note: in call to Cpp function here [InCallToCppFunction]
   // CHECK:STDERR:   v.ref_ref_this();
   // CHECK:STDERR:   ^~~~~~~~~~~~~~~~
   // CHECK:STDERR:
   v.ref_ref_this();
 
-  // CHECK:STDERR: fail_bad_5891_object_param_qualifiers_by_value.carbon:[[@LINE+7]]:3: error: semantics TODO: `Unsupported: object parameter type: const struct HasQualifiers &&` [SemanticsTodo]
+  // CHECK:STDERR: fail_bad_object_param_qualifiers_by_value.carbon:[[@LINE+7]]:3: error: semantics TODO: `Unsupported: object parameter type: const struct HasQualifiers &&` [SemanticsTodo]
   // CHECK:STDERR:   v.const_ref_ref_this();
   // CHECK:STDERR:   ^~~~~~~~~~~~~~~~~~~~~~
-  // CHECK:STDERR: fail_bad_5891_object_param_qualifiers_by_value.carbon:[[@LINE+4]]:3: note: in call to Cpp function here [InCallToCppFunction]
+  // CHECK:STDERR: fail_bad_object_param_qualifiers_by_value.carbon:[[@LINE+4]]:3: note: in call to Cpp function here [InCallToCppFunction]
   // CHECK:STDERR:   v.const_ref_ref_this();
   // CHECK:STDERR:   ^~~~~~~~~~~~~~~~~~~~~~
   // CHECK:STDERR:
@@ -180,7 +148,7 @@ struct ExplicitObjectParam {
   void H(this Another);
 };
 
-// --- fail_todo_5891_call_explicit_object_param.carbon
+// --- call_explicit_object_param.carbon
 
 library "[[@TEST_NAME]]";
 
@@ -188,36 +156,13 @@ import Cpp library "explicit_object_param.h";
 
 fn Call(e: Cpp.ExplicitObjectParam, n: i32, a: Cpp.Another) {
   //@dump-sem-ir-begin
-  // CHECK:STDERR: fail_todo_5891_call_explicit_object_param.carbon:[[@LINE+5]]:3: error: missing object argument in method call [MissingObjectInMethodCall]
-  // CHECK:STDERR:   e.F();
-  // CHECK:STDERR:   ^~~~~
-  // CHECK:STDERR: fail_todo_5891_call_explicit_object_param.carbon: note: calling function declared here [InCallToFunction]
-  // CHECK:STDERR:
   e.F();
-  // CHECK:STDERR: fail_todo_5891_call_explicit_object_param.carbon:[[@LINE+9]]:3: error: member name of type `<type of Cpp.G>` in compound member access is not an instance member or an interface member [CompoundMemberAccessDoesNotUseBase]
-  // CHECK:STDERR:   n.(Cpp.ExplicitObjectParam.G)();
-  // CHECK:STDERR:   ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-  // CHECK:STDERR:
-  // CHECK:STDERR: fail_todo_5891_call_explicit_object_param.carbon:[[@LINE+5]]:3: error: missing object argument in method call [MissingObjectInMethodCall]
-  // CHECK:STDERR:   n.(Cpp.ExplicitObjectParam.G)();
-  // CHECK:STDERR:   ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-  // CHECK:STDERR: fail_todo_5891_call_explicit_object_param.carbon: note: calling function declared here [InCallToFunction]
-  // CHECK:STDERR:
   n.(Cpp.ExplicitObjectParam.G)();
-  // CHECK:STDERR: fail_todo_5891_call_explicit_object_param.carbon:[[@LINE+9]]:3: error: member name of type `<type of Cpp.H>` in compound member access is not an instance member or an interface member [CompoundMemberAccessDoesNotUseBase]
-  // CHECK:STDERR:   a.(Cpp.ExplicitObjectParam.H)();
-  // CHECK:STDERR:   ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-  // CHECK:STDERR:
-  // CHECK:STDERR: fail_todo_5891_call_explicit_object_param.carbon:[[@LINE+5]]:3: error: missing object argument in method call [MissingObjectInMethodCall]
-  // CHECK:STDERR:   a.(Cpp.ExplicitObjectParam.H)();
-  // CHECK:STDERR:   ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-  // CHECK:STDERR: fail_todo_5891_call_explicit_object_param.carbon: note: calling function declared here [InCallToFunction]
-  // CHECK:STDERR:
   a.(Cpp.ExplicitObjectParam.H)();
   //@dump-sem-ir-end
 }
 
-// CHECK:STDOUT: --- fail_todo_5891_use_object_param_qualifiers.carbon
+// CHECK:STDOUT: --- use_object_param_qualifiers.carbon
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %HasQualifiers: type = class_type @HasQualifiers [concrete]
@@ -272,46 +217,58 @@ fn Call(e: Cpp.ExplicitObjectParam, n: i32, a: Cpp.Another) {
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F(%v.param: %HasQualifiers, %p.param: %ptr.ec3) {
 // CHECK:STDOUT: !entry:
-// CHECK:STDOUT:   %v.ref.loc13: %HasQualifiers = name_ref v, %v
-// CHECK:STDOUT:   %const_this.ref.loc13: %.602 = name_ref const_this, imports.%.ce8 [concrete = constants.%empty_struct.63b]
-// CHECK:STDOUT:   %addr.loc13: %ptr.ec3 = addr_of <error> [concrete = <error>]
-// CHECK:STDOUT:   %.loc13_16.1: %ptr.2cb = as_compatible %addr.loc13 [concrete = <error>]
-// CHECK:STDOUT:   %.loc13_16.2: %ptr.2cb = converted %addr.loc13, %.loc13_16.1 [concrete = <error>]
-// CHECK:STDOUT:   %const_this__carbon_thunk.call.loc13: init %empty_tuple.type = call imports.%const_this__carbon_thunk.decl(%.loc13_16.2)
-// CHECK:STDOUT:   %v.ref.loc19: %HasQualifiers = name_ref v, %v
-// CHECK:STDOUT:   %const_ref_this.ref.loc19: %.bf0 = name_ref const_ref_this, imports.%.667 [concrete = constants.%empty_struct.4f2]
-// CHECK:STDOUT:   %addr.loc19: %ptr.ec3 = addr_of <error> [concrete = <error>]
-// CHECK:STDOUT:   %.loc19_20.1: %ptr.2cb = as_compatible %addr.loc19 [concrete = <error>]
-// CHECK:STDOUT:   %.loc19_20.2: %ptr.2cb = converted %addr.loc19, %.loc19_20.1 [concrete = <error>]
-// CHECK:STDOUT:   %const_ref_this__carbon_thunk.call.loc19: init %empty_tuple.type = call imports.%const_ref_this__carbon_thunk.decl(%.loc19_20.2)
-// CHECK:STDOUT:   %p.ref.loc26: %ptr.ec3 = name_ref p, %p
-// CHECK:STDOUT:   %.loc26: ref %HasQualifiers = deref %p.ref.loc26
+// CHECK:STDOUT:   %v.ref.loc8: %HasQualifiers = name_ref v, %v
+// CHECK:STDOUT:   %const_this.ref.loc8: %.602 = name_ref const_this, imports.%.ce8 [concrete = constants.%empty_struct.63b]
+// CHECK:STDOUT:   %bound_method.loc8: <bound method> = bound_method %v.ref.loc8, %const_this.ref.loc8
+// CHECK:STDOUT:   %.loc8_3: ref %HasQualifiers = value_as_ref %v.ref.loc8
+// CHECK:STDOUT:   %addr.loc8: %ptr.ec3 = addr_of %.loc8_3
+// CHECK:STDOUT:   %.loc8_16.1: %ptr.2cb = as_compatible %addr.loc8
+// CHECK:STDOUT:   %.loc8_16.2: %ptr.2cb = converted %addr.loc8, %.loc8_16.1
+// CHECK:STDOUT:   %const_this__carbon_thunk.call.loc8: init %empty_tuple.type = call imports.%const_this__carbon_thunk.decl(%.loc8_16.2)
+// CHECK:STDOUT:   %v.ref.loc9: %HasQualifiers = name_ref v, %v
+// CHECK:STDOUT:   %const_ref_this.ref.loc9: %.bf0 = name_ref const_ref_this, imports.%.667 [concrete = constants.%empty_struct.4f2]
+// CHECK:STDOUT:   %bound_method.loc9: <bound method> = bound_method %v.ref.loc9, %const_ref_this.ref.loc9
+// CHECK:STDOUT:   %.loc9_3: ref %HasQualifiers = value_as_ref %v.ref.loc9
+// CHECK:STDOUT:   %addr.loc9: %ptr.ec3 = addr_of %.loc9_3
+// CHECK:STDOUT:   %.loc9_20.1: %ptr.2cb = as_compatible %addr.loc9
+// CHECK:STDOUT:   %.loc9_20.2: %ptr.2cb = converted %addr.loc9, %.loc9_20.1
+// CHECK:STDOUT:   %const_ref_this__carbon_thunk.call.loc9: init %empty_tuple.type = call imports.%const_ref_this__carbon_thunk.decl(%.loc9_20.2)
+// CHECK:STDOUT:   %p.ref.loc11: %ptr.ec3 = name_ref p, %p
+// CHECK:STDOUT:   %.loc11: ref %HasQualifiers = deref %p.ref.loc11
 // CHECK:STDOUT:   %plain.ref: %.64b = name_ref plain, imports.%.646 [concrete = constants.%empty_struct.a83]
-// CHECK:STDOUT:   <elided>
-// CHECK:STDOUT:   %HasQualifiers.plain.call: init %empty_tuple.type = call imports.%HasQualifiers.plain.decl(<error>)
-// CHECK:STDOUT:   %p.ref.loc32: %ptr.ec3 = name_ref p, %p
-// CHECK:STDOUT:   %.loc32: ref %HasQualifiers = deref %p.ref.loc32
+// CHECK:STDOUT:   %bound_method.loc11: <bound method> = bound_method %.loc11, %plain.ref
+// CHECK:STDOUT:   %addr.loc11: %ptr.ec3 = addr_of %.loc11
+// CHECK:STDOUT:   %HasQualifiers.plain.call: init %empty_tuple.type = call imports.%HasQualifiers.plain.decl(%addr.loc11)
+// CHECK:STDOUT:   %p.ref.loc12: %ptr.ec3 = name_ref p, %p
+// CHECK:STDOUT:   %.loc12: ref %HasQualifiers = deref %p.ref.loc12
 // CHECK:STDOUT:   %ref_this.ref: %.352 = name_ref ref_this, imports.%.145 [concrete = constants.%empty_struct.f58]
-// CHECK:STDOUT:   <elided>
-// CHECK:STDOUT:   %HasQualifiers.ref_this.call: init %empty_tuple.type = call imports.%HasQualifiers.ref_this.decl(<error>)
-// CHECK:STDOUT:   %p.ref.loc38: %ptr.ec3 = name_ref p, %p
-// CHECK:STDOUT:   %.loc38_4: ref %HasQualifiers = deref %p.ref.loc38
-// CHECK:STDOUT:   %const_this.ref.loc38: %.602 = name_ref const_this, imports.%.ce8 [concrete = constants.%empty_struct.63b]
-// CHECK:STDOUT:   %addr.loc38: %ptr.ec3 = addr_of <error> [concrete = <error>]
-// CHECK:STDOUT:   %.loc38_17.1: %ptr.2cb = as_compatible %addr.loc38 [concrete = <error>]
-// CHECK:STDOUT:   %.loc38_17.2: %ptr.2cb = converted %addr.loc38, %.loc38_17.1 [concrete = <error>]
-// CHECK:STDOUT:   %const_this__carbon_thunk.call.loc38: init %empty_tuple.type = call imports.%const_this__carbon_thunk.decl(%.loc38_17.2)
-// CHECK:STDOUT:   %p.ref.loc44: %ptr.ec3 = name_ref p, %p
-// CHECK:STDOUT:   %.loc44_4: ref %HasQualifiers = deref %p.ref.loc44
-// CHECK:STDOUT:   %const_ref_this.ref.loc44: %.bf0 = name_ref const_ref_this, imports.%.667 [concrete = constants.%empty_struct.4f2]
-// CHECK:STDOUT:   %addr.loc44: %ptr.ec3 = addr_of <error> [concrete = <error>]
-// CHECK:STDOUT:   %.loc44_21.1: %ptr.2cb = as_compatible %addr.loc44 [concrete = <error>]
-// CHECK:STDOUT:   %.loc44_21.2: %ptr.2cb = converted %addr.loc44, %.loc44_21.1 [concrete = <error>]
-// CHECK:STDOUT:   %const_ref_this__carbon_thunk.call.loc44: init %empty_tuple.type = call imports.%const_ref_this__carbon_thunk.decl(%.loc44_21.2)
+// CHECK:STDOUT:   %bound_method.loc12: <bound method> = bound_method %.loc12, %ref_this.ref
+// CHECK:STDOUT:   %addr.loc12: %ptr.ec3 = addr_of %.loc12
+// CHECK:STDOUT:   %HasQualifiers.ref_this.call: init %empty_tuple.type = call imports.%HasQualifiers.ref_this.decl(%addr.loc12)
+// CHECK:STDOUT:   %p.ref.loc13: %ptr.ec3 = name_ref p, %p
+// CHECK:STDOUT:   %.loc13_4.1: ref %HasQualifiers = deref %p.ref.loc13
+// CHECK:STDOUT:   %const_this.ref.loc13: %.602 = name_ref const_this, imports.%.ce8 [concrete = constants.%empty_struct.63b]
+// CHECK:STDOUT:   %bound_method.loc13: <bound method> = bound_method %.loc13_4.1, %const_this.ref.loc13
+// CHECK:STDOUT:   %.loc13_4.2: %HasQualifiers = bind_value %.loc13_4.1
+// CHECK:STDOUT:   %.loc13_4.3: ref %HasQualifiers = value_as_ref %.loc13_4.2
+// CHECK:STDOUT:   %addr.loc13: %ptr.ec3 = addr_of %.loc13_4.3
+// CHECK:STDOUT:   %.loc13_17.1: %ptr.2cb = as_compatible %addr.loc13
+// CHECK:STDOUT:   %.loc13_17.2: %ptr.2cb = converted %addr.loc13, %.loc13_17.1
+// CHECK:STDOUT:   %const_this__carbon_thunk.call.loc13: init %empty_tuple.type = call imports.%const_this__carbon_thunk.decl(%.loc13_17.2)
+// CHECK:STDOUT:   %p.ref.loc14: %ptr.ec3 = name_ref p, %p
+// CHECK:STDOUT:   %.loc14_4.1: ref %HasQualifiers = deref %p.ref.loc14
+// CHECK:STDOUT:   %const_ref_this.ref.loc14: %.bf0 = name_ref const_ref_this, imports.%.667 [concrete = constants.%empty_struct.4f2]
+// CHECK:STDOUT:   %bound_method.loc14: <bound method> = bound_method %.loc14_4.1, %const_ref_this.ref.loc14
+// CHECK:STDOUT:   %.loc14_4.2: %HasQualifiers = bind_value %.loc14_4.1
+// CHECK:STDOUT:   %.loc14_4.3: ref %HasQualifiers = value_as_ref %.loc14_4.2
+// CHECK:STDOUT:   %addr.loc14: %ptr.ec3 = addr_of %.loc14_4.3
+// CHECK:STDOUT:   %.loc14_21.1: %ptr.2cb = as_compatible %addr.loc14
+// CHECK:STDOUT:   %.loc14_21.2: %ptr.2cb = converted %addr.loc14, %.loc14_21.1
+// CHECK:STDOUT:   %const_ref_this__carbon_thunk.call.loc14: init %empty_tuple.type = call imports.%const_ref_this__carbon_thunk.decl(%.loc14_21.2)
 // CHECK:STDOUT:   <elided>
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
-// CHECK:STDOUT: --- fail_todo_5891_call_explicit_object_param.carbon
+// CHECK:STDOUT: --- call_explicit_object_param.carbon
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %ExplicitObjectParam: type = class_type @ExplicitObjectParam [concrete]
@@ -367,19 +324,24 @@ fn Call(e: Cpp.ExplicitObjectParam, n: i32, a: Cpp.Another) {
 // CHECK:STDOUT: !entry:
 // CHECK:STDOUT:   %e.ref: %ExplicitObjectParam = name_ref e, %e
 // CHECK:STDOUT:   %F.ref: %.3e2 = name_ref F, imports.%.037 [concrete = constants.%empty_struct.48d]
-// CHECK:STDOUT:   %addr.loc13: %ptr.7f5 = addr_of <error> [concrete = <error>]
-// CHECK:STDOUT:   %F__carbon_thunk.call: init %empty_tuple.type = call imports.%F__carbon_thunk.decl(%addr.loc13)
+// CHECK:STDOUT:   %bound_method.loc8: <bound method> = bound_method %e.ref, %F.ref
+// CHECK:STDOUT:   %.loc8: ref %ExplicitObjectParam = value_as_ref %e.ref
+// CHECK:STDOUT:   %addr.loc8: %ptr.7f5 = addr_of %.loc8
+// CHECK:STDOUT:   %F__carbon_thunk.call: init %empty_tuple.type = call imports.%F__carbon_thunk.decl(%addr.loc8)
 // CHECK:STDOUT:   %n.ref: %i32 = name_ref n, %n
-// CHECK:STDOUT:   %Cpp.ref.loc23: <namespace> = name_ref Cpp, imports.%Cpp [concrete = imports.%Cpp]
-// CHECK:STDOUT:   %ExplicitObjectParam.ref.loc23: type = name_ref ExplicitObjectParam, imports.%ExplicitObjectParam.decl [concrete = constants.%ExplicitObjectParam]
+// CHECK:STDOUT:   %Cpp.ref.loc9: <namespace> = name_ref Cpp, imports.%Cpp [concrete = imports.%Cpp]
+// CHECK:STDOUT:   %ExplicitObjectParam.ref.loc9: type = name_ref ExplicitObjectParam, imports.%ExplicitObjectParam.decl [concrete = constants.%ExplicitObjectParam]
 // CHECK:STDOUT:   %G.ref: %.d44 = name_ref G, imports.%.151 [concrete = constants.%empty_struct.a7c]
-// CHECK:STDOUT:   %ExplicitObjectParam.G.call: init %empty_tuple.type = call imports.%ExplicitObjectParam.G.decl(<error>)
+// CHECK:STDOUT:   %bound_method.loc9: <bound method> = bound_method %n.ref, %G.ref
+// CHECK:STDOUT:   %ExplicitObjectParam.G.call: init %empty_tuple.type = call imports.%ExplicitObjectParam.G.decl(%n.ref)
 // CHECK:STDOUT:   %a.ref: %Another = name_ref a, %a
-// CHECK:STDOUT:   %Cpp.ref.loc33: <namespace> = name_ref Cpp, imports.%Cpp [concrete = imports.%Cpp]
-// CHECK:STDOUT:   %ExplicitObjectParam.ref.loc33: type = name_ref ExplicitObjectParam, imports.%ExplicitObjectParam.decl [concrete = constants.%ExplicitObjectParam]
+// CHECK:STDOUT:   %Cpp.ref.loc10: <namespace> = name_ref Cpp, imports.%Cpp [concrete = imports.%Cpp]
+// CHECK:STDOUT:   %ExplicitObjectParam.ref.loc10: type = name_ref ExplicitObjectParam, imports.%ExplicitObjectParam.decl [concrete = constants.%ExplicitObjectParam]
 // CHECK:STDOUT:   %H.ref: %.9fb = name_ref H, imports.%.34a [concrete = constants.%empty_struct.b14]
-// CHECK:STDOUT:   %addr.loc33: %ptr.289 = addr_of <error> [concrete = <error>]
-// CHECK:STDOUT:   %H__carbon_thunk.call: init %empty_tuple.type = call imports.%H__carbon_thunk.decl(%addr.loc33)
+// CHECK:STDOUT:   %bound_method.loc10: <bound method> = bound_method %a.ref, %H.ref
+// CHECK:STDOUT:   %.loc10: ref %Another = value_as_ref %a.ref
+// CHECK:STDOUT:   %addr.loc10: %ptr.289 = addr_of %.loc10
+// CHECK:STDOUT:   %H__carbon_thunk.call: init %empty_tuple.type = call imports.%H__carbon_thunk.decl(%addr.loc10)
 // CHECK:STDOUT:   <elided>
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/interop/cpp/class/struct.carbon b/toolchain/check/testdata/interop/cpp/class/struct.carbon
index e52d96278aca..e1fcaed70581 100644
--- a/toolchain/check/testdata/interop/cpp/class/struct.carbon
+++ b/toolchain/check/testdata/interop/cpp/class/struct.carbon
@@ -514,6 +514,7 @@ fn MyF(bar: Cpp.Bar*);
 // CHECK:STDOUT:   %bar.ref: %ptr.f68 = name_ref bar, %bar
 // CHECK:STDOUT:   %.loc15: ref %Bar = deref %bar.ref
 // CHECK:STDOUT:   %f.ref: %.2e2 = name_ref f, imports.%.6e0 [concrete = constants.%empty_struct]
+// CHECK:STDOUT:   %bound_method: <bound method> = bound_method %.loc15, %f.ref
 // CHECK:STDOUT:   return
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/interop/cpp/class/template.carbon b/toolchain/check/testdata/interop/cpp/class/template.carbon
index 5b270d7e2515..404cbae1859e 100644
--- a/toolchain/check/testdata/interop/cpp/class/template.carbon
+++ b/toolchain/check/testdata/interop/cpp/class/template.carbon
@@ -10,8 +10,6 @@
 // TIP: To dump output, run:
 // TIP:   bazel run //toolchain/testing:file_test -- --dump_output --file_tests=toolchain/check/testdata/interop/cpp/class/template.carbon
 
-// TODO: Tests marked as `fail_todo_5891_` to fixed as a follow-up of https://github.com/carbon-language/carbon-lang/pull/5891.
-
 // --- class_template.h
 
 struct Base {};
@@ -24,7 +22,7 @@ template<typename T> struct A : Base {
 using Aint = A<int>;
 using Along = A<long>;
 
-// --- fail_todo_5891_use_class_template.carbon
+// --- use_class_template.carbon
 
 library "[[@TEST_NAME]]";
 
@@ -33,11 +31,6 @@ import Cpp library "class_template.h";
 fn F(x: Cpp.Aint) -> i32 {
   // Trigger instantiation through name lookup.
   //@dump-sem-ir-begin
-  // CHECK:STDERR: fail_todo_5891_use_class_template.carbon:[[@LINE+5]]:3: error: missing object argument in method call [MissingObjectInMethodCall]
-  // CHECK:STDERR:   x.f();
-  // CHECK:STDERR:   ^~~~~
-  // CHECK:STDERR: fail_todo_5891_use_class_template.carbon: note: calling function declared here [InCallToFunction]
-  // CHECK:STDERR:
   x.f();
   return x.n;
   //@dump-sem-ir-end
@@ -87,7 +80,7 @@ var x: Cpp.XY.r#type = 0;
 var y: Cpp.Xint.r#type = 0;
 //@dump-sem-ir-end
 
-// CHECK:STDOUT: --- fail_todo_5891_use_class_template.carbon
+// CHECK:STDOUT: --- use_class_template.carbon
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %A.0bedf0.1: type = class_type @A.1 [concrete]
@@ -143,36 +136,38 @@ var y: Cpp.Xint.r#type = 0;
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @F(%x.param: %A.0bedf0.1) -> %i32 {
 // CHECK:STDOUT: !entry:
-// CHECK:STDOUT:   %x.ref.loc14: %A.0bedf0.1 = name_ref x, %x
+// CHECK:STDOUT:   %x.ref.loc9: %A.0bedf0.1 = name_ref x, %x
 // CHECK:STDOUT:   %f.ref: %.658 = name_ref f, imports.%.d46 [concrete = constants.%empty_struct]
-// CHECK:STDOUT:   %addr: %ptr.270828.1 = addr_of <error> [concrete = <error>]
-// CHECK:STDOUT:   %.loc14_7.1: %ptr.703 = as_compatible %addr [concrete = <error>]
-// CHECK:STDOUT:   %.loc14_7.2: %ptr.703 = converted %addr, %.loc14_7.1 [concrete = <error>]
-// CHECK:STDOUT:   %f__carbon_thunk.call: init %empty_tuple.type = call imports.%f__carbon_thunk.decl(%.loc14_7.2)
-// CHECK:STDOUT:   %x.ref.loc15: %A.0bedf0.1 = name_ref x, %x
+// CHECK:STDOUT:   %bound_method.loc9: <bound method> = bound_method %x.ref.loc9, %f.ref
+// CHECK:STDOUT:   %.loc9_3: ref %A.0bedf0.1 = value_as_ref %x.ref.loc9
+// CHECK:STDOUT:   %addr: %ptr.270828.1 = addr_of %.loc9_3
+// CHECK:STDOUT:   %.loc9_7.1: %ptr.703 = as_compatible %addr
+// CHECK:STDOUT:   %.loc9_7.2: %ptr.703 = converted %addr, %.loc9_7.1
+// CHECK:STDOUT:   %f__carbon_thunk.call: init %empty_tuple.type = call imports.%f__carbon_thunk.decl(%.loc9_7.2)
+// CHECK:STDOUT:   %x.ref.loc10: %A.0bedf0.1 = name_ref x, %x
 // CHECK:STDOUT:   %n.ref: %A.elem.c3f = name_ref n, @A.1.%.2 [concrete = @A.1.%.2]
-// CHECK:STDOUT:   %.loc15_11.1: ref %i32 = class_element_access %x.ref.loc15, element1
-// CHECK:STDOUT:   %.loc15_11.2: %i32 = bind_value %.loc15_11.1
+// CHECK:STDOUT:   %.loc10_11.1: ref %i32 = class_element_access %x.ref.loc10, element1
+// CHECK:STDOUT:   %.loc10_11.2: %i32 = bind_value %.loc10_11.1
 // CHECK:STDOUT:   %impl.elem0: %.7fa = impl_witness_access constants.%Copy.impl_witness.a32, element0 [concrete = constants.%Int.as.Copy.impl.Op.f59]
-// CHECK:STDOUT:   %bound_method.loc15_11.1: <bound method> = bound_method %.loc15_11.2, %impl.elem0
+// CHECK:STDOUT:   %bound_method.loc10_11.1: <bound method> = bound_method %.loc10_11.2, %impl.elem0
 // CHECK:STDOUT:   %specific_fn: <specific function> = specific_function %impl.elem0, @Int.as.Copy.impl.Op(constants.%int_32) [concrete = constants.%Int.as.Copy.impl.Op.specific_fn]
-// CHECK:STDOUT:   %bound_method.loc15_11.2: <bound method> = bound_method %.loc15_11.2, %specific_fn
-// CHECK:STDOUT:   %Int.as.Copy.impl.Op.call: init %i32 = call %bound_method.loc15_11.2(%.loc15_11.2)
+// CHECK:STDOUT:   %bound_method.loc10_11.2: <bound method> = bound_method %.loc10_11.2, %specific_fn
+// CHECK:STDOUT:   %Int.as.Copy.impl.Op.call: init %i32 = call %bound_method.loc10_11.2(%.loc10_11.2)
 // CHECK:STDOUT:   return %Int.as.Copy.impl.Op.call to %return
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
 // CHECK:STDOUT: fn @G(%p.param: %ptr.270828.2) -> %ptr.fb2 {
 // CHECK:STDOUT: !entry:
 // CHECK:STDOUT:   %p.ref: %ptr.270828.2 = name_ref p, %p
-// CHECK:STDOUT:   %.loc22_11.1: ref %A.0bedf0.2 = deref %p.ref
-// CHECK:STDOUT:   %.loc22_11.2: ref %Base = class_element_access %.loc22_11.1, element0
-// CHECK:STDOUT:   %addr: %ptr.fb2 = addr_of %.loc22_11.2
-// CHECK:STDOUT:   %.loc22_11.3: %ptr.fb2 = converted %p.ref, %addr
+// CHECK:STDOUT:   %.loc17_11.1: ref %A.0bedf0.2 = deref %p.ref
+// CHECK:STDOUT:   %.loc17_11.2: ref %Base = class_element_access %.loc17_11.1, element0
+// CHECK:STDOUT:   %addr: %ptr.fb2 = addr_of %.loc17_11.2
+// CHECK:STDOUT:   %.loc17_11.3: %ptr.fb2 = converted %p.ref, %addr
 // CHECK:STDOUT:   %impl.elem0: %.e43 = impl_witness_access constants.%Copy.impl_witness.fe1, element0 [concrete = constants.%ptr.as.Copy.impl.Op.07b]
-// CHECK:STDOUT:   %bound_method.loc22_11.1: <bound method> = bound_method %.loc22_11.3, %impl.elem0
+// CHECK:STDOUT:   %bound_method.loc17_11.1: <bound method> = bound_method %.loc17_11.3, %impl.elem0
 // CHECK:STDOUT:   %specific_fn: <specific function> = specific_function %impl.elem0, @ptr.as.Copy.impl.Op(constants.%Base) [concrete = constants.%ptr.as.Copy.impl.Op.specific_fn]
-// CHECK:STDOUT:   %bound_method.loc22_11.2: <bound method> = bound_method %.loc22_11.3, %specific_fn
-// CHECK:STDOUT:   %ptr.as.Copy.impl.Op.call: init %ptr.fb2 = call %bound_method.loc22_11.2(%.loc22_11.3)
+// CHECK:STDOUT:   %bound_method.loc17_11.2: <bound method> = bound_method %.loc17_11.3, %specific_fn
+// CHECK:STDOUT:   %ptr.as.Copy.impl.Op.call: init %ptr.fb2 = call %bound_method.loc17_11.2(%.loc17_11.3)
 // CHECK:STDOUT:   return %ptr.as.Copy.impl.Op.call to %return
 // CHECK:STDOUT: }
 // CHECK:STDOUT:
diff --git a/toolchain/check/testdata/interop/cpp/enum/anonymous.carbon b/toolchain/check/testdata/interop/cpp/enum/anonymous.carbon
index e37a506ab8ba..aec87d9be2c8 100644
--- a/toolchain/check/testdata/interop/cpp/enum/anonymous.carbon
+++ b/toolchain/check/testdata/interop/cpp/enum/anonymous.carbon
@@ -10,8 +10,6 @@
 // TIP: To dump output, run:
 // TIP:   bazel run //toolchain/testing:file_test -- --dump_output --file_tests=toolchain/check/testdata/interop/cpp/enum/anonymous.carbon
 
-// TODO: Tests marked as `fail_todo_5891_` to fixed as a follow-up of https://github.com/carbon-language/carbon-lang/pull/5891.
-
 // --- anon.h
 
 enum { a, b, c };
@@ -25,7 +23,7 @@ class C {
   void F(decltype(d));
 };
 
-// --- fail_todo_5891_copy_enum.carbon
+// --- copy_enum.carbon
 
 library "[[@TEST_NAME]]";
 
@@ -35,16 +33,11 @@ import Cpp library "anon.h";
 fn G() {
   Cpp.F(Cpp.b);
 
-  // CHECK:STDERR: fail_todo_5891_copy_enum.carbon:[[@LINE+5]]:3: error: missing object argument in method call [MissingObjectInMethodCall]
-  // CHECK:STDERR:   Cpp.C.C().F(Cpp.C.e);
-  // CHECK:STDERR:   ^~~~~~~~~~~~~~~~~~~~
-  // CHECK:STDERR: fail_todo_5891_copy_enum.carbon: note: calling function declared here [InCallToFunction]
-  // CHECK:STDERR:
   Cpp.C.C().F(Cpp.C.e);
 }
 //@dump-sem-ir-end
 
-// CHECK:STDOUT: --- fail_todo_5891_copy_enum.carbon
+// CHECK:STDOUT: --- copy_enum.carbon
 // CHECK:STDOUT:
 // CHECK:STDOUT: constants {
 // CHECK:STDOUT:   %G.type: type = fn_type @G [concrete]
@@ -122,33 +115,34 @@ fn G() {
 // CHECK:STDOUT:   %.loc8_12.2: ref %.4f0 = temporary %.loc8_12.1, %b.ref
 // CHECK:STDOUT:   %addr.loc8_14: %ptr.793 = addr_of %.loc8_12.2
 // CHECK:STDOUT:   %F__carbon_thunk.call.loc8: init %empty_tuple.type = call imports.%F__carbon_thunk.decl.e1b8ec.1(%addr.loc8_14)
-// CHECK:STDOUT:   %Cpp.ref.loc15_3: <namespace> = name_ref Cpp, imports.%Cpp [concrete = imports.%Cpp]
-// CHECK:STDOUT:   %C.ref.loc15_6: type = name_ref C, imports.%C.decl [concrete = constants.%C]
-// CHECK:STDOUT:   %C.ref.loc15_8: %.d40 = name_ref C, imports.%.40b [concrete = constants.%empty_struct.e73]
-// CHECK:STDOUT:   %.loc15_11.1: ref %C = temporary_storage
-// CHECK:STDOUT:   %addr.loc15_11.1: %ptr.d9e = addr_of %.loc15_11.1
-// CHECK:STDOUT:   %C__carbon_thunk.call: init %empty_tuple.type = call imports.%C__carbon_thunk.decl(%addr.loc15_11.1)
-// CHECK:STDOUT:   %.loc15_11.2: init %C = in_place_init %C__carbon_thunk.call, %.loc15_11.1
-// CHECK:STDOUT:   %.loc15_11.3: ref %C = temporary %.loc15_11.1, %.loc15_11.2
-// CHECK:STDOUT:   %F.ref.loc15: %.9a3 = name_ref F, imports.%.951 [concrete = constants.%empty_struct.acc]
-// CHECK:STDOUT:   %Cpp.ref.loc15_15: <namespace> = name_ref Cpp, imports.%Cpp [concrete = imports.%Cpp]
-// CHECK:STDOUT:   %C.ref.loc15_18: type = name_ref C, imports.%C.decl [concrete = constants.%C]
+// CHECK:STDOUT:   %Cpp.ref.loc10_3: <namespace> = name_ref Cpp, imports.%Cpp [concrete = imports.%Cpp]
+// CHECK:STDOUT:   %C.ref.loc10_6: type = name_ref C, imports.%C.decl [concrete = constants.%C]
+// CHECK:STDOUT:   %C.ref.loc10_8: %.d40 = name_ref C, imports.%.40b [concrete = constants.%empty_struct.e73]
+// CHECK:STDOUT:   %.loc10_11.1: ref %C = temporary_storage
+// CHECK:STDOUT:   %addr.loc10_11.1: %ptr.d9e = addr_of %.loc10_11.1
+// CHECK:STDOUT:   %C__carbon_thunk.call: init %empty_tuple.type = call imports.%C__carbon_thunk.decl(%addr.loc10_11.1)
+// CHECK:STDOUT:   %.loc10_11.2: init %C = in_place_init %C__carbon_thunk.call, %.loc10_11.1
+// CHECK:STDOUT:   %.loc10_11.3: ref %C = temporary %.loc10_11.1, %.loc10_11.2
+// CHECK:STDOUT:   %F.ref.loc10: %.9a3 = name_ref F, imports.%.951 [concrete = constants.%empty_struct.acc]
+// CHECK:STDOUT:   %bound_method.loc10_12: <bound method> = bound_method %.loc10_11.3, %F.ref.loc10
+// CHECK:STDOUT:   %Cpp.ref.loc10_15: <namespace> = name_ref Cpp, imports.%Cpp [concrete = imports.%Cpp]
+// CHECK:STDOUT:   %C.ref.loc10_18: type = name_ref C, imports.%C.decl [concrete = constants.%C]
 // CHECK:STDOUT:   %e.ref: %.bb7 = name_ref e, imports.%int_1.1d6 [concrete = constants.%int_1.1d6]
+// CHECK:STDOUT:   %addr.loc10_11.2: %ptr.d9e = addr_of %.loc10_11.3
+// CHECK:STDOUT:   %.loc10_20.1: ref %.bb7 = temporary_storage
+// CHECK:STDOUT:   %.loc10_20.2: ref %.bb7 = temporary %.loc10_20.1, %e.ref
+// CHECK:STDOUT:   %addr.loc10_22: %ptr.73d = addr_of %.loc10_20.2
+// CHECK:STDOUT:   %F__carbon_thunk.call.loc10: init %empty_tuple.type = call imports.%F__carbon_thunk.decl.e1b8ec.2(%addr.loc10_11.2, %addr.loc10_22)
+// CHECK:STDOUT:   %T.as.Destroy.impl.Op.bound.loc10_20: <bound method> = bound_method %.loc10_20.2, constants.%T.as.Destroy.impl.Op.bd3
 // CHECK:STDOUT:   <elided>
-// CHECK:STDOUT:   %.loc15_20.1: ref %.bb7 = temporary_storage
-// CHECK:STDOUT:   %.loc15_20.2: ref %.bb7 = temporary %.loc15_20.1, %e.ref
-// CHECK:STDOUT:   %addr.loc15_22: %ptr.73d = addr_of %.loc15_20.2
-// CHECK:STDOUT:   %F__carbon_thunk.call.loc15: init %empty_tuple.type = call imports.%F__carbon_thunk.decl.e1b8ec.2(<error>, %addr.loc15_22)
-// CHECK:STDOUT:   %T.as.Destroy.impl.Op.bound.loc15_20: <bound method> = bound_method %.loc15_20.2, constants.%T.as.Destroy.impl.Op.bd3
+// CHECK:STDOUT:   %bound_method.loc10_20: <bound method> = bound_method %.loc10_20.2, %T.as.Destroy.impl.Op.specific_fn.1
+// CHECK:STDOUT:   %addr.loc10_20: %ptr.73d = addr_of %.loc10_20.2
+// CHECK:STDOUT:   %T.as.Destroy.impl.Op.call.loc10_20: init %empty_tuple.type = call %bound_method.loc10_20(%addr.loc10_20)
+// CHECK:STDOUT:   %T.as.Destroy.impl.Op.bound.loc10_11: <bound method> = bound_method %.loc10_11.3, constants.%T.as.Destroy.impl.Op.a28
 // CHECK:STDOUT:   <elided>
-// CHECK:STDOUT:   %bound_method.loc15_20: <bound method> = bound_method %.loc15_20.2, %T.as.Destroy.impl.Op.specific_fn.1
-// CHECK:STDOUT:   %addr.loc15_20: %ptr.73d = addr_of %.loc15_20.2
-// CHECK:STDOUT:   %T.as.Destroy.impl.Op.call.loc15_20: init %empty_tuple.type = call %bound_method.loc15_20(%addr.loc15_20)
-// CHECK:STDOUT:   %T.as.Destroy.impl.Op.bound.loc15_11: <bound method> = bound_method %.loc15_11.3, constants.%T.as.Destroy.impl.Op.a28
-// CHECK:STDOUT:   <elided>
-// CHECK:STDOUT:   %bound_method.loc15_11: <bound method> = bound_method %.loc15_11.3, %T.as.Destroy.impl.Op.specific_fn.2
-// CHECK:STDOUT:   %addr.loc15_11.2: %ptr.d9e = addr_of %.loc15_11.3
-// CHECK:STDOUT:   %T.as.Destroy.impl.Op.call.loc15_11: init %empty_tuple.type = call %bound_method.loc15_11(%addr.loc15_11.2)
+// CHECK:STDOUT:   %bound_method.loc10_11: <bound method> = bound_method %.loc10_11.3, %T.as.Destroy.impl.Op.specific_fn.2
+// CHECK:STDOUT:   %addr.loc10_11.3: %ptr.d9e = addr_of %.loc10_11.3
+// CHECK:STDOUT:   %T.as.Destroy.impl.Op.call.loc10_11: init %empty_tuple.type = call %bound_method.loc10_11(%addr.loc10_11.3)
 // CHECK:STDOUT:   %T.as.Destroy.impl.Op.bound.loc8: <bound method> = bound_method %.loc8_12.2, constants.%T.as.Destroy.impl.Op.dda
 // CHECK:STDOUT:   <elided>
 // CHECK:STDOUT:   %bound_method.loc8: <bound method> = bound_method %.loc8_12.2, %T.as.Destroy.impl.Op.specific_fn.3
diff --git a/toolchain/lower/testdata/interop/cpp/base.carbon b/toolchain/lower/testdata/interop/cpp/base.carbon
index 4c9cb9026db0..5a1a20199e7e 100644
--- a/toolchain/lower/testdata/interop/cpp/base.carbon
+++ b/toolchain/lower/testdata/interop/cpp/base.carbon
@@ -10,8 +10,6 @@
 // TIP: To dump output, run:
 // TIP:   bazel run //toolchain/testing:file_test -- --dump_output --file_tests=toolchain/lower/testdata/interop/cpp/base.carbon
 
-// TODO: Tests marked as `fail_todo_5891_` to fixed as a follow-up of https://github.com/carbon-language/carbon-lang/pull/5891.
-
 // --- structs.h
 
 struct A {
@@ -50,17 +48,119 @@ fn AccessVal(b: Cpp.B) -> i32 {
   return b.a;
 }
 
-// --- fail_todo_5891_call_method.carbon
+// --- call_method.carbon
 
 library "[[@TEST_NAME]]";
 
 import Cpp library "structs.h";
 
 fn Call(b: Cpp.B*) {
-  // CHECK:STDERR: fail_todo_5891_call_method.carbon:[[@LINE+5]]:3: error: missing object argument in method call [MissingObjectInMethodCall]
-  // CHECK:STDERR:   b->f();
-  // CHECK:STDERR:   ^~~~~~
-  // CHECK:STDERR: fail_todo_5891_call_method.carbon: note: calling function declared here [InCallToFunction]
-  // CHECK:STDERR:
   b->f();
 }
+
+// CHECK:STDOUT: ; ModuleID = 'convert.carbon'
+// CHECK:STDOUT: source_filename = "convert.carbon"
+// CHECK:STDOUT: target datalayout = "e-m:e-p270:32:32-p271:32:32-p272:64:64-i64:64-i128:128-f80:128-n8:16:32:64-S128"
+// CHECK:STDOUT: target triple = "x86_64-unknown-linux-gnu"
+// CHECK:STDOUT:
+// CHECK:STDOUT: define ptr @_CConvertPtr.Main(ptr %p) !dbg !7 {
+// CHECK:STDOUT: entry:
+// CHECK:STDOUT:   %.loc7_11.2.base = getelementptr inbounds nuw [8 x i8], ptr %p, i32 0, i32 0, !dbg !10
+// CHECK:STDOUT:   ret ptr %.loc7_11.2.base, !dbg !10
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: declare void @_CAcceptVal.Main(ptr)
+// CHECK:STDOUT:
+// CHECK:STDOUT: define void @_CConvertVal.Main(ptr %b) !dbg !11 {
+// CHECK:STDOUT: entry:
+// CHECK:STDOUT:   %.loc13_13.1.base = getelementptr inbounds nuw [8 x i8], ptr %b, i32 0, i32 0, !dbg !12
+// CHECK:STDOUT:   call void @_CAcceptVal.Main(ptr %.loc13_13.1.base), !dbg !13
+// CHECK:STDOUT:   ret void, !dbg !14
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: !llvm.module.flags = !{!0, !1, !2, !3, !4}
+// CHECK:STDOUT: !llvm.dbg.cu = !{!5}
+// CHECK:STDOUT:
+// CHECK:STDOUT: !0 = !{i32 7, !"Dwarf Version", i32 5}
+// CHECK:STDOUT: !1 = !{i32 2, !"Debug Info Version", i32 3}
+// CHECK:STDOUT: !2 = !{i32 1, !"wchar_size", i32 4}
+// CHECK:STDOUT: !3 = !{i32 8, !"PIC Level", i32 0}
+// CHECK:STDOUT: !4 = !{i32 7, !"PIE Level", i32 2}
+// CHECK:STDOUT: !5 = distinct !DICompileUnit(language: DW_LANG_C, file: !6, producer: "carbon", isOptimized: false, runtimeVersion: 0, emissionKind: FullDebug)
+// CHECK:STDOUT: !6 = !DIFile(filename: "convert.carbon", directory: "")
+// CHECK:STDOUT: !7 = distinct !DISubprogram(name: "ConvertPtr", linkageName: "_CConvertPtr.Main", scope: null, file: !6, line: 6, type: !8, spFlags: DISPFlagDefinition, unit: !5)
+// CHECK:STDOUT: !8 = !DISubroutineType(types: !9)
+// CHECK:STDOUT: !9 = !{}
+// CHECK:STDOUT: !10 = !DILocation(line: 7, column: 3, scope: !7)
+// CHECK:STDOUT: !11 = distinct !DISubprogram(name: "ConvertVal", linkageName: "_CConvertVal.Main", scope: null, file: !6, line: 12, type: !8, spFlags: DISPFlagDefinition, unit: !5)
+// CHECK:STDOUT: !12 = !DILocation(line: 13, column: 13, scope: !11)
+// CHECK:STDOUT: !13 = !DILocation(line: 13, column: 3, scope: !11)
+// CHECK:STDOUT: !14 = !DILocation(line: 12, column: 1, scope: !11)
+// CHECK:STDOUT: ; ModuleID = 'access_field.carbon'
+// CHECK:STDOUT: source_filename = "access_field.carbon"
+// CHECK:STDOUT: target datalayout = "e-m:e-p270:32:32-p271:32:32-p272:64:64-i64:64-i128:128-f80:128-n8:16:32:64-S128"
+// CHECK:STDOUT: target triple = "x86_64-unknown-linux-gnu"
+// CHECK:STDOUT:
+// CHECK:STDOUT: define i32 @_CAccessVal.Main(ptr %b) !dbg !7 {
+// CHECK:STDOUT: entry:
+// CHECK:STDOUT:   %.loc7_11.1.base = getelementptr inbounds nuw [8 x i8], ptr %b, i32 0, i32 0, !dbg !10
+// CHECK:STDOUT:   %.loc7_11.3.a = getelementptr inbounds nuw [4 x i8], ptr %.loc7_11.1.base, i32 0, i32 0, !dbg !10
+// CHECK:STDOUT:   %.loc7_11.4 = load i32, ptr %.loc7_11.3.a, align 4, !dbg !10
+// CHECK:STDOUT:   ret i32 %.loc7_11.4, !dbg !11
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: !llvm.module.flags = !{!0, !1, !2, !3, !4}
+// CHECK:STDOUT: !llvm.dbg.cu = !{!5}
+// CHECK:STDOUT:
+// CHECK:STDOUT: !0 = !{i32 7, !"Dwarf Version", i32 5}
+// CHECK:STDOUT: !1 = !{i32 2, !"Debug Info Version", i32 3}
+// CHECK:STDOUT: !2 = !{i32 1, !"wchar_size", i32 4}
+// CHECK:STDOUT: !3 = !{i32 8, !"PIC Level", i32 0}
+// CHECK:STDOUT: !4 = !{i32 7, !"PIE Level", i32 2}
+// CHECK:STDOUT: !5 = distinct !DICompileUnit(language: DW_LANG_C, file: !6, producer: "carbon", isOptimized: false, runtimeVersion: 0, emissionKind: FullDebug)
+// CHECK:STDOUT: !6 = !DIFile(filename: "access_field.carbon", directory: "")
+// CHECK:STDOUT: !7 = distinct !DISubprogram(name: "AccessVal", linkageName: "_CAccessVal.Main", scope: null, file: !6, line: 6, type: !8, spFlags: DISPFlagDefinition, unit: !5)
+// CHECK:STDOUT: !8 = !DISubroutineType(types: !9)
+// CHECK:STDOUT: !9 = !{}
+// CHECK:STDOUT: !10 = !DILocation(line: 7, column: 10, scope: !7)
+// CHECK:STDOUT: !11 = !DILocation(line: 7, column: 3, scope: !7)
+// CHECK:STDOUT: ; ModuleID = 'call_method.carbon'
+// CHECK:STDOUT: source_filename = "call_method.carbon"
+// CHECK:STDOUT: target datalayout = "e-m:e-p270:32:32-p271:32:32-p272:64:64-i64:64-i128:128-f80:128-n8:16:32:64-S128"
+// CHECK:STDOUT: target triple = "x86_64-unknown-linux-gnu"
+// CHECK:STDOUT:
+// CHECK:STDOUT: $_ZN1A1fEv = comdat any
+// CHECK:STDOUT:
+// CHECK:STDOUT: define void @_CCall.Main(ptr %b) !dbg !7 {
+// CHECK:STDOUT: entry:
+// CHECK:STDOUT:   %.loc7_4.3.base = getelementptr inbounds nuw [8 x i8], ptr %b, i32 0, i32 0, !dbg !10
+// CHECK:STDOUT:   call void @_ZN1A1fEv(ptr %.loc7_4.3.base), !dbg !10
+// CHECK:STDOUT:   ret void, !dbg !11
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: ; Function Attrs: mustprogress noinline nounwind optnone
+// CHECK:STDOUT: define linkonce_odr dso_local void @_ZN1A1fEv(ptr nonnull align 4 dereferenceable(4) %this) #0 comdat align 2 {
+// CHECK:STDOUT: entry:
+// CHECK:STDOUT:   %this.addr = alloca ptr, align 8
+// CHECK:STDOUT:   store ptr %this, ptr %this.addr, align 8
+// CHECK:STDOUT:   %this1 = load ptr, ptr %this.addr, align 8
+// CHECK:STDOUT:   ret void
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: attributes #0 = { mustprogress noinline nounwind optnone "min-legal-vector-width"="0" "no-trapping-math"="true" "stack-protector-buffer-size"="0" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
+// CHECK:STDOUT:
+// CHECK:STDOUT: !llvm.module.flags = !{!0, !1, !2, !3, !4}
+// CHECK:STDOUT: !llvm.dbg.cu = !{!5}
+// CHECK:STDOUT:
+// CHECK:STDOUT: !0 = !{i32 7, !"Dwarf Version", i32 5}
+// CHECK:STDOUT: !1 = !{i32 2, !"Debug Info Version", i32 3}
+// CHECK:STDOUT: !2 = !{i32 1, !"wchar_size", i32 4}
+// CHECK:STDOUT: !3 = !{i32 8, !"PIC Level", i32 0}
+// CHECK:STDOUT: !4 = !{i32 7, !"PIE Level", i32 2}
+// CHECK:STDOUT: !5 = distinct !DICompileUnit(language: DW_LANG_C, file: !6, producer: "carbon", isOptimized: false, runtimeVersion: 0, emissionKind: FullDebug)
+// CHECK:STDOUT: !6 = !DIFile(filename: "call_method.carbon", directory: "")
+// CHECK:STDOUT: !7 = distinct !DISubprogram(name: "Call", linkageName: "_CCall.Main", scope: null, file: !6, line: 6, type: !8, spFlags: DISPFlagDefinition, unit: !5)
+// CHECK:STDOUT: !8 = !DISubroutineType(types: !9)
+// CHECK:STDOUT: !9 = !{}
+// CHECK:STDOUT: !10 = !DILocation(line: 7, column: 3, scope: !7)
+// CHECK:STDOUT: !11 = !DILocation(line: 6, column: 1, scope: !7)
diff --git a/toolchain/lower/testdata/interop/cpp/method.carbon b/toolchain/lower/testdata/interop/cpp/method.carbon
index 1e71456b14ab..209f9379727e 100644
--- a/toolchain/lower/testdata/interop/cpp/method.carbon
+++ b/toolchain/lower/testdata/interop/cpp/method.carbon
@@ -11,8 +11,6 @@
 // TIP: To dump output, run:
 // TIP:   bazel run //toolchain/testing:file_test -- --dump_output --file_tests=toolchain/lower/testdata/interop/cpp/method.carbon
 
-// TODO: Tests marked as `fail_todo_5891_` to fixed as a follow-up of https://github.com/carbon-language/carbon-lang/pull/5891.
-
 // --- methods.h
 
 struct A {
@@ -21,33 +19,23 @@ struct A {
   int n;
 };
 
-// --- fail_todo_5891_call_by_val.carbon
+// --- call_by_val.carbon
 
 library "[[@TEST_NAME]]";
 
 import Cpp library "methods.h";
 
 fn UseVal(a: Cpp.A) -> i32 {
-  // CHECK:STDERR: fail_todo_5891_call_by_val.carbon:[[@LINE+5]]:10: error: missing object argument in method call [MissingObjectInMethodCall]
-  // CHECK:STDERR:   return a.by_val();
-  // CHECK:STDERR:          ^~~~~~~~~~
-  // CHECK:STDERR: fail_todo_5891_call_by_val.carbon: note: calling function declared here [InCallToFunction]
-  // CHECK:STDERR:
   return a.by_val();
 }
 
-// --- fail_todo_5891_call_by_ref.carbon
+// --- call_by_ref.carbon
 
 library "[[@TEST_NAME]]";
 
 import Cpp library "methods.h";
 
 fn UseVal(a: Cpp.A*) -> i32 {
-  // CHECK:STDERR: fail_todo_5891_call_by_ref.carbon:[[@LINE+5]]:10: error: missing object argument in method call [MissingObjectInMethodCall]
-  // CHECK:STDERR:   return a->by_ref();
-  // CHECK:STDERR:          ^~~~~~~~~~~
-  // CHECK:STDERR: fail_todo_5891_call_by_ref.carbon: note: calling function declared here [InCallToFunction]
-  // CHECK:STDERR:
   return a->by_ref();
 }
 
@@ -58,23 +46,191 @@ struct NeedThunk {
   void Explicit(this NeedThunk, signed char c);
 };
 
-// --- fail_todo_5891_call_thunk.carbon
+// --- call_thunk.carbon
 
 library "[[@TEST_NAME]]";
 
 import Cpp library "thunk.h";
 
 fn Call(n: Cpp.NeedThunk) {
-  // CHECK:STDERR: fail_todo_5891_call_thunk.carbon:[[@LINE+5]]:3: error: missing object argument in method call [MissingObjectInMethodCall]
-  // CHECK:STDERR:   n.Implicit(1);
-  // CHECK:STDERR:   ^~~~~~~~~~~~~
-  // CHECK:STDERR: fail_todo_5891_call_thunk.carbon: note: calling function declared here [InCallToFunction]
-  // CHECK:STDERR:
   n.Implicit(1);
-  // CHECK:STDERR: fail_todo_5891_call_thunk.carbon:[[@LINE+5]]:3: error: missing object argument in method call [MissingObjectInMethodCall]
-  // CHECK:STDERR:   n.Explicit(1);
-  // CHECK:STDERR:   ^~~~~~~~~~~~~
-  // CHECK:STDERR: fail_todo_5891_call_thunk.carbon: note: calling function declared here [InCallToFunction]
-  // CHECK:STDERR:
   n.Explicit(1);
 }
+
+// CHECK:STDOUT: ; ModuleID = 'call_by_val.carbon'
+// CHECK:STDOUT: source_filename = "call_by_val.carbon"
+// CHECK:STDOUT: target datalayout = "e-m:e-p270:32:32-p271:32:32-p272:64:64-i64:64-i128:128-f80:128-n8:16:32:64-S128"
+// CHECK:STDOUT: target triple = "x86_64-unknown-linux-gnu"
+// CHECK:STDOUT:
+// CHECK:STDOUT: %struct.A = type { i32 }
+// CHECK:STDOUT:
+// CHECK:STDOUT: $_ZNK1A6by_valEv = comdat any
+// CHECK:STDOUT:
+// CHECK:STDOUT: define i32 @_CUseVal.Main(ptr %a) !dbg !7 {
+// CHECK:STDOUT: entry:
+// CHECK:STDOUT:   %by_val__carbon_thunk.call = call i32 @_ZNK1A6by_valEv.carbon_thunk(ptr %a), !dbg !10
+// CHECK:STDOUT:   ret i32 %by_val__carbon_thunk.call, !dbg !11
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: ; Function Attrs: mustprogress noinline nounwind optnone
+// CHECK:STDOUT: define linkonce_odr dso_local i32 @_ZNK1A6by_valEv(ptr nonnull align 4 dereferenceable(4) %this) #0 comdat align 2 {
+// CHECK:STDOUT: entry:
+// CHECK:STDOUT:   %this.addr = alloca ptr, align 8
+// CHECK:STDOUT:   store ptr %this, ptr %this.addr, align 8
+// CHECK:STDOUT:   %this1 = load ptr, ptr %this.addr, align 8
+// CHECK:STDOUT:   %n = getelementptr inbounds nuw %struct.A, ptr %this1, i32 0, i32 0
+// CHECK:STDOUT:   %0 = load i32, ptr %n, align 4
+// CHECK:STDOUT:   ret i32 %0
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: ; Function Attrs: alwaysinline mustprogress
+// CHECK:STDOUT: define dso_local i32 @_ZNK1A6by_valEv.carbon_thunk(ptr %this) #1 {
+// CHECK:STDOUT: entry:
+// CHECK:STDOUT:   %this.addr = alloca ptr, align 8
+// CHECK:STDOUT:   store ptr %this, ptr %this.addr, align 8
+// CHECK:STDOUT:   %0 = load ptr, ptr %this.addr, align 8
+// CHECK:STDOUT:   %call = call i32 @_ZNK1A6by_valEv(ptr nonnull align 4 dereferenceable(4) %0)
+// CHECK:STDOUT:   ret i32 %call
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: attributes #0 = { mustprogress noinline nounwind optnone "min-legal-vector-width"="0" "no-trapping-math"="true" "stack-protector-buffer-size"="0" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
+// CHECK:STDOUT: attributes #1 = { alwaysinline mustprogress "min-legal-vector-width"="0" "no-trapping-math"="true" "stack-protector-buffer-size"="0" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
+// CHECK:STDOUT:
+// CHECK:STDOUT: !llvm.module.flags = !{!0, !1, !2, !3, !4}
+// CHECK:STDOUT: !llvm.dbg.cu = !{!5}
+// CHECK:STDOUT:
+// CHECK:STDOUT: !0 = !{i32 7, !"Dwarf Version", i32 5}
+// CHECK:STDOUT: !1 = !{i32 2, !"Debug Info Version", i32 3}
+// CHECK:STDOUT: !2 = !{i32 1, !"wchar_size", i32 4}
+// CHECK:STDOUT: !3 = !{i32 8, !"PIC Level", i32 0}
+// CHECK:STDOUT: !4 = !{i32 7, !"PIE Level", i32 2}
+// CHECK:STDOUT: !5 = distinct !DICompileUnit(language: DW_LANG_C, file: !6, producer: "carbon", isOptimized: false, runtimeVersion: 0, emissionKind: FullDebug)
+// CHECK:STDOUT: !6 = !DIFile(filename: "call_by_val.carbon", directory: "")
+// CHECK:STDOUT: !7 = distinct !DISubprogram(name: "UseVal", linkageName: "_CUseVal.Main", scope: null, file: !6, line: 6, type: !8, spFlags: DISPFlagDefinition, unit: !5)
+// CHECK:STDOUT: !8 = !DISubroutineType(types: !9)
+// CHECK:STDOUT: !9 = !{}
+// CHECK:STDOUT: !10 = !DILocation(line: 7, column: 10, scope: !7)
+// CHECK:STDOUT: !11 = !DILocation(line: 7, column: 3, scope: !7)
+// CHECK:STDOUT: ; ModuleID = 'call_by_ref.carbon'
+// CHECK:STDOUT: source_filename = "call_by_ref.carbon"
+// CHECK:STDOUT: target datalayout = "e-m:e-p270:32:32-p271:32:32-p272:64:64-i64:64-i128:128-f80:128-n8:16:32:64-S128"
+// CHECK:STDOUT: target triple = "x86_64-unknown-linux-gnu"
+// CHECK:STDOUT:
+// CHECK:STDOUT: %struct.A = type { i32 }
+// CHECK:STDOUT:
+// CHECK:STDOUT: $_ZN1A6by_refEv = comdat any
+// CHECK:STDOUT:
+// CHECK:STDOUT: define i32 @_CUseVal.Main(ptr %a) !dbg !7 {
+// CHECK:STDOUT: entry:
+// CHECK:STDOUT:   %A.by_ref.call = call i32 @_ZN1A6by_refEv(ptr %a), !dbg !10
+// CHECK:STDOUT:   ret i32 %A.by_ref.call, !dbg !11
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: ; Function Attrs: mustprogress noinline nounwind optnone
+// CHECK:STDOUT: define linkonce_odr dso_local i32 @_ZN1A6by_refEv(ptr nonnull align 4 dereferenceable(4) %this) #0 comdat align 2 {
+// CHECK:STDOUT: entry:
+// CHECK:STDOUT:   %this.addr = alloca ptr, align 8
+// CHECK:STDOUT:   store ptr %this, ptr %this.addr, align 8
+// CHECK:STDOUT:   %this1 = load ptr, ptr %this.addr, align 8
+// CHECK:STDOUT:   %n = getelementptr inbounds nuw %struct.A, ptr %this1, i32 0, i32 0
+// CHECK:STDOUT:   %0 = load i32, ptr %n, align 4
+// CHECK:STDOUT:   ret i32 %0
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: attributes #0 = { mustprogress noinline nounwind optnone "min-legal-vector-width"="0" "no-trapping-math"="true" "stack-protector-buffer-size"="0" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
+// CHECK:STDOUT:
+// CHECK:STDOUT: !llvm.module.flags = !{!0, !1, !2, !3, !4}
+// CHECK:STDOUT: !llvm.dbg.cu = !{!5}
+// CHECK:STDOUT:
+// CHECK:STDOUT: !0 = !{i32 7, !"Dwarf Version", i32 5}
+// CHECK:STDOUT: !1 = !{i32 2, !"Debug Info Version", i32 3}
+// CHECK:STDOUT: !2 = !{i32 1, !"wchar_size", i32 4}
+// CHECK:STDOUT: !3 = !{i32 8, !"PIC Level", i32 0}
+// CHECK:STDOUT: !4 = !{i32 7, !"PIE Level", i32 2}
+// CHECK:STDOUT: !5 = distinct !DICompileUnit(language: DW_LANG_C, file: !6, producer: "carbon", isOptimized: false, runtimeVersion: 0, emissionKind: FullDebug)
+// CHECK:STDOUT: !6 = !DIFile(filename: "call_by_ref.carbon", directory: "")
+// CHECK:STDOUT: !7 = distinct !DISubprogram(name: "UseVal", linkageName: "_CUseVal.Main", scope: null, file: !6, line: 6, type: !8, spFlags: DISPFlagDefinition, unit: !5)
+// CHECK:STDOUT: !8 = !DISubroutineType(types: !9)
+// CHECK:STDOUT: !9 = !{}
+// CHECK:STDOUT: !10 = !DILocation(line: 7, column: 10, scope: !7)
+// CHECK:STDOUT: !11 = !DILocation(line: 7, column: 3, scope: !7)
+// CHECK:STDOUT: ; ModuleID = 'call_thunk.carbon'
+// CHECK:STDOUT: source_filename = "call_thunk.carbon"
+// CHECK:STDOUT: target datalayout = "e-m:e-p270:32:32-p271:32:32-p272:64:64-i64:64-i128:128-f80:128-n8:16:32:64-S128"
+// CHECK:STDOUT: target triple = "x86_64-unknown-linux-gnu"
+// CHECK:STDOUT:
+// CHECK:STDOUT: %struct.NeedThunk = type { i8 }
+// CHECK:STDOUT:
+// CHECK:STDOUT: define void @_CCall.Main(ptr %n) !dbg !7 {
+// CHECK:STDOUT: entry:
+// CHECK:STDOUT:   %.loc7_14.3.temp = alloca i8, align 1, !dbg !10
+// CHECK:STDOUT:   %.loc8_14.3.temp = alloca i8, align 1, !dbg !11
+// CHECK:STDOUT:   call void @llvm.lifetime.start.p0(ptr %.loc7_14.3.temp), !dbg !10
+// CHECK:STDOUT:   store i8 1, ptr %.loc7_14.3.temp, align 1, !dbg !10
+// CHECK:STDOUT:   call void @_ZNK9NeedThunk8ImplicitEa.carbon_thunk(ptr %n, ptr %.loc7_14.3.temp), !dbg !12
+// CHECK:STDOUT:   call void @llvm.lifetime.start.p0(ptr %.loc8_14.3.temp), !dbg !11
+// CHECK:STDOUT:   store i8 1, ptr %.loc8_14.3.temp, align 1, !dbg !11
+// CHECK:STDOUT:   call void @_ZNH9NeedThunk8ExplicitES_a.carbon_thunk(ptr %n, ptr %.loc8_14.3.temp), !dbg !13
+// CHECK:STDOUT:   ret void, !dbg !14
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: declare void @_ZNK9NeedThunk8ImplicitEa(ptr, i8)
+// CHECK:STDOUT:
+// CHECK:STDOUT: declare void @_ZNH9NeedThunk8ExplicitES_a(ptr, i8)
+// CHECK:STDOUT:
+// CHECK:STDOUT: ; Function Attrs: nocallback nofree nosync nounwind willreturn memory(argmem: readwrite)
+// CHECK:STDOUT: declare void @llvm.lifetime.start.p0(ptr captures(none)) #0
+// CHECK:STDOUT:
+// CHECK:STDOUT: ; Function Attrs: alwaysinline mustprogress
+// CHECK:STDOUT: define dso_local void @_ZNK9NeedThunk8ImplicitEa.carbon_thunk(ptr %this, ptr %c) #1 {
+// CHECK:STDOUT: entry:
+// CHECK:STDOUT:   %this.addr = alloca ptr, align 8
+// CHECK:STDOUT:   %c.addr = alloca ptr, align 8
+// CHECK:STDOUT:   store ptr %this, ptr %this.addr, align 8
+// CHECK:STDOUT:   store ptr %c, ptr %c.addr, align 8
+// CHECK:STDOUT:   %0 = load ptr, ptr %this.addr, align 8
+// CHECK:STDOUT:   %1 = load ptr, ptr %c.addr, align 8
+// CHECK:STDOUT:   %2 = load i8, ptr %1, align 1
+// CHECK:STDOUT:   call void @_ZNK9NeedThunk8ImplicitEa(ptr nonnull align 1 dereferenceable(1) %0, i8 signext %2)
+// CHECK:STDOUT:   ret void
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: ; Function Attrs: alwaysinline mustprogress
+// CHECK:STDOUT: define dso_local void @_ZNH9NeedThunk8ExplicitES_a.carbon_thunk(ptr %0, ptr %c) #1 {
+// CHECK:STDOUT: entry:
+// CHECK:STDOUT:   %.addr = alloca ptr, align 8
+// CHECK:STDOUT:   %c.addr = alloca ptr, align 8
+// CHECK:STDOUT:   %agg.tmp = alloca %struct.NeedThunk, align 1
+// CHECK:STDOUT:   store ptr %0, ptr %.addr, align 8
+// CHECK:STDOUT:   store ptr %c, ptr %c.addr, align 8
+// CHECK:STDOUT:   %1 = load ptr, ptr %.addr, align 8
+// CHECK:STDOUT:   %2 = load ptr, ptr %c.addr, align 8
+// CHECK:STDOUT:   %3 = load i8, ptr %2, align 1
+// CHECK:STDOUT:   call void @_ZNH9NeedThunk8ExplicitES_a(i8 signext %3)
+// CHECK:STDOUT:   ret void
+// CHECK:STDOUT: }
+// CHECK:STDOUT:
+// CHECK:STDOUT: ; uselistorder directives
+// CHECK:STDOUT: uselistorder ptr @llvm.lifetime.start.p0, { 1, 0 }
+// CHECK:STDOUT:
+// CHECK:STDOUT: attributes #0 = { nocallback nofree nosync nounwind willreturn memory(argmem: readwrite) }
+// CHECK:STDOUT: attributes #1 = { alwaysinline mustprogress "min-legal-vector-width"="0" "no-trapping-math"="true" "stack-protector-buffer-size"="0" "target-cpu"="x86-64" "target-features"="+cmov,+cx8,+fxsr,+mmx,+sse,+sse2,+x87" "tune-cpu"="generic" }
+// CHECK:STDOUT:
+// CHECK:STDOUT: !llvm.module.flags = !{!0, !1, !2, !3, !4}
+// CHECK:STDOUT: !llvm.dbg.cu = !{!5}
+// CHECK:STDOUT:
+// CHECK:STDOUT: !0 = !{i32 7, !"Dwarf Version", i32 5}
+// CHECK:STDOUT: !1 = !{i32 2, !"Debug Info Version", i32 3}
+// CHECK:STDOUT: !2 = !{i32 1, !"wchar_size", i32 4}
+// CHECK:STDOUT: !3 = !{i32 8, !"PIC Level", i32 0}
+// CHECK:STDOUT: !4 = !{i32 7, !"PIE Level", i32 2}
+// CHECK:STDOUT: !5 = distinct !DICompileUnit(language: DW_LANG_C, file: !6, producer: "carbon", isOptimized: false, runtimeVersion: 0, emissionKind: FullDebug)
+// CHECK:STDOUT: !6 = !DIFile(filename: "call_thunk.carbon", directory: "")
+// CHECK:STDOUT: !7 = distinct !DISubprogram(name: "Call", linkageName: "_CCall.Main", scope: null, file: !6, line: 6, type: !8, spFlags: DISPFlagDefinition, unit: !5)
+// CHECK:STDOUT: !8 = !DISubroutineType(types: !9)
+// CHECK:STDOUT: !9 = !{}
+// CHECK:STDOUT: !10 = !DILocation(line: 7, column: 14, scope: !7)
+// CHECK:STDOUT: !11 = !DILocation(line: 8, column: 14, scope: !7)
+// CHECK:STDOUT: !12 = !DILocation(line: 7, column: 3, scope: !7)
+// CHECK:STDOUT: !13 = !DILocation(line: 8, column: 3, scope: !7)
+// CHECK:STDOUT: !14 = !DILocation(line: 6, column: 1, scope: !7)