You'll need to wait until sometime next year to play Marvel's Avengers in its full glory on PlayStation 5 and Xbox Series X/S. The game won't be fully optimized for those consoles until 2021. Crystal Dynamics and Square Enix previously said the upgrade (which is free for those who bought the game on PS4/Xbox One) would be available during the holiday season.
Crystal Dynamics studio head Scot Amos that the decision was made "to ensure that we give our team the time to deliver a next-gen experience showcasing all that this game is meant to be." You'll still be able to play the PS4 or Xbox One versions on their sibling consoles, and they'll get a couple of boosts in the form of higher frame rates and faster loading times. You can carry forward your game save data and still play co-op missions with friends on the respective older console.