If there is not enough space on the hard drive, you may encounter the Call of Duty Vanguard not launching PS5 issue. So, you'd better check and free disk space on the PS5 system. You can access the Settings menu from the Home screen and navigate to Storage, and then delete all unnecessary game cache, add-ons, and apps.
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.