Yes, you can play almost all PS4 games (physical and digital) on the PS5 as well. And this game is one of many that is compatible for backwards compatibility on PS5. Sorry, there was a problem.
Call of Duty: Vanguard - Has crossplay between PS4, PS5, Xbox One, Xbox Series X/S and PC. Cross-progression is also enabled. Call of Duty: Warzone - Full crossplay support across PS4, PS5, Xbox One, Xbox Series X/S and PC.