We are just days away from the Playstation 5 to be available to the public, with that being said
Earlier today Sony confirmed via a Playstation 5 Ultimate blog, that you will soon be able to store but not play your PS5 games on an external drive after a future update coming to the console.

No, players cannot transfer PS5 games to a USB drive. PS5 games must be stored on the console’s internal ultra-high speed SSD for gameplay. Explorations for allowing players to store (but not play) PS5 games on a USB drive in a future update are underway.
Additionally, Sony confirmed that in near future they will update us on our M.2 SSD expansion will work and with which drives.
This M.2 SSD storage upgrade functionality will come to PS5 after launch as part of a system software update. We’ll share more details in the future, including around which type of M.2 SSD storage drive will be compatible with PS5.
We can’t wait to hear what Sony will reveal in the future! Don’t forget to check out our PS5 review