Can PS5 games by played on a PS4?

Want to get two games and wondering as the prices are almost the same for ps4 and ps5 if the ps4 version can be played on a ps5 or should I go for a cheap download version in the meantime? Cant see any offers on Black Friday for these games.


Assassin's Creed Valhalla
Cold War Call of Duty

Seems a waste to be paying full price for PS4 when will be on PS5 within a year?

Any advice please, thanks