diff --git a/include/pybind11/detail/init.h b/include/pybind11/detail/init.h
index b7f8d5a52..102b37cab 100644
--- a/include/pybind11/detail/init.h
+++ b/include/pybind11/detail/init.h
@@ -370,8 +370,15 @@ template <typename CFunc,
 struct factory;
 
 // Specialization for py::init(Func)
+// Note: The 4th template parameter `void_type()` is explicitly specified to resolve a
+// template ambiguity with the dual-factory specialization below when compiled with
+// nvcc + GCC (see #5565). Without it, both specializations match equally well for the
+// single-factory case, since the 4th parameter defaults to
+// `function_signature_t<void_type(*)()>` = `void_type()`, which the dual-factory
+// specialization can also decompose as `AReturn(AArgs...)` with `AReturn=void_type`
+// and `AArgs={}`.
 template <typename Func, typename Return, typename... Args>
-struct factory<Func, void_type (*)(), Return(Args...)> {
+struct factory<Func, void_type (*)(), Return(Args...), void_type()> {
     remove_reference_t<Func> class_factory;
 
     // NOLINTNEXTLINE(google-explicit-constructor)