PS5 games cannot be played from an external USB drive as these are much slower than the internal SSD drive. PS5 games must be stored on the console’s internal ultra-high speed SSD for gameplay. And for the moment, PS5 games cannot be transferred to external drives for storage, either.
Sony is looking into allowing players to store (but not play) PS5 games on a USB drive in a future update. This will be enabled via a firmware update once available.
You can store and play PS4 games from a compatible USB drive connected to PS5. In fact, Sony recommends this approach to save space on the internal console storage for PS5 games, which can’t be played off an extended storage drive.
Players can also set a system preference on PS5 that will, by default, install all PS4 games (including digital purchases from PlayStation Store, and game data from Blu-ray discs) and future game patches directly to a connected USB drive.