Sadly, the two God of War games that were released for the PlayStation Portable  Chains of Olympus and Ghost of Sparta  are currently not playable on the PlayStation 5.

If you don't have a PlayStation 3 for the compiled versions, God of War, God of War II, God of War III, God of War: Ascension, God of War: Chains of Olympus and God of War: Ghost of Sparta, all are available as part of the PlayStation Now service.