diff --git a/include/nlohmann/detail/conversions/to_json.hpp b/include/nlohmann/detail/conversions/to_json.hpp
index 491bb9873..fb48e4f82 100644
--- a/include/nlohmann/detail/conversions/to_json.hpp
+++ b/include/nlohmann/detail/conversions/to_json.hpp
@@ -287,7 +287,7 @@ struct external_constructor<value_t::object>
 #ifdef JSON_HAS_CPP_17
 template<typename BasicJsonType, typename T,
          enable_if_t<std::is_constructible<BasicJsonType, T>::value, int> = 0>
-void to_json(BasicJsonType& j, const std::optional<T>& opt) noexcept
+void to_json(BasicJsonType& j, const std::optional<T>& opt) noexcept(std::is_nothrow_assignable<BasicJsonType&, const T&>::value)
 {
     if (opt.has_value())
     {
diff --git a/single_include/nlohmann/json.hpp b/single_include/nlohmann/json.hpp
index 6c98e7a8f..a606e1762 100644
--- a/single_include/nlohmann/json.hpp
+++ b/single_include/nlohmann/json.hpp
@@ -6820,7 +6820,7 @@ struct external_constructor<value_t::object>
 #ifdef JSON_HAS_CPP_17
 template<typename BasicJsonType, typename T,
          enable_if_t<std::is_constructible<BasicJsonType, T>::value, int> = 0>
-void to_json(BasicJsonType& j, const std::optional<T>& opt) noexcept
+void to_json(BasicJsonType& j, const std::optional<T>& opt) noexcept(std::is_nothrow_assignable<BasicJsonType&, const T&>::value)
 {
     if (opt.has_value())
     {
diff --git a/tests/src/unit-conversions.cpp b/tests/src/unit-conversions.cpp
index 077ba0e14..0d53f2226 100644
--- a/tests/src/unit-conversions.cpp
+++ b/tests/src/unit-conversions.cpp
@@ -1834,6 +1834,21 @@ TEST_CASE("std::u8string")
 #endif
 #endif
 
+#if !defined(JSON_NOEXCEPTION)
+namespace
+{
+// a type whose to_json reports an error by throwing, used below to check that
+// converting a std::optional<T> to JSON propagates an exception thrown while
+// converting its contained value instead of calling std::terminate (#5642)
+struct throwing_to_json_type {};
+
+[[noreturn]] void to_json(json& /*unused*/, const throwing_to_json_type& /*unused*/)
+{
+    throw std::runtime_error("cannot serialize throwing_to_json_type");
+}
+}  // namespace
+#endif
+
 TEST_CASE("std::optional")
 {
     SECTION("null")
@@ -1916,6 +1931,23 @@ TEST_CASE("std::optional")
         CHECK(json(opt_object) == j_object);
         CHECK(std::map<std::string, std::optional<int>>(j_object) == opt_object);
     }
+
+#if !defined(JSON_NOEXCEPTION)
+    SECTION("exception from contained value's to_json propagates (#5642)")
+    {
+        // to_json(BasicJsonType&, const std::optional<T>&) must not be
+        // noexcept: it calls T's to_json, which may throw (a user-defined
+        // to_json that reports an error, or std::bad_alloc for T =
+        // std::string/vector/json). Before the fix, this called
+        // std::terminate() instead of letting the exception propagate.
+        const std::optional<throwing_to_json_type> opt = throwing_to_json_type{};
+        CHECK_THROWS_WITH_AS(json(opt), "cannot serialize throwing_to_json_type", std::runtime_error&);
+
+        // the conversion is noexcept exactly when converting the contained value is
+        static_assert(!std::is_nothrow_constructible<json, const std::optional<throwing_to_json_type>&>::value, "");
+        static_assert(std::is_nothrow_constructible<json, const std::optional<int>&>::value, "");
+    }
+#endif
 }
 #endif