UPDATE: Sony recently confirmed that PS5 games can't be stored on HDDs in a recent FAQ post:
"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."
Sony's next-gen PlayStation 5 games can only be stored on SSDs, and can't be migrated to or downloaded directly onto HDDs.
Storage space is a premium commodity for game consoles. The PS5's high-speed PCIe 4.0 SSD can push 5.5GB/sec speeds, but its space is constrained more than usual. The system's 812GB SSD only has about 667GB of usable space, and with titles like Black Ops Cold War clocking in at 133GB, gamers will feel the squeeze on day one. External drives are going to be very, very important for next-gen.
There's just one big problem: Next-gen PS5 games can't be stored on an HDD. You can't use your beefy 2TB external HDD as cold storage for your next-gen PS5 games. According to Press Start, only PS4 games can be stored on an HDD, and it appears PS5 games are exclusive to SSDs. The website didn't try hooking up an external SSD to the PS5 though, so that would be worth a shot.
Also remember the PS5 won't support expansion M.2 SSDs at launch, so keep that in mind. The M.2 expansion bay is currently turned off and will be activated with a future firmware patch.
This is disappointing news. We knew PS5 games couldn't be booted from an HDD, but there was an assumption gamers could use a combination of external HDDs and the built-in SSD to cycle-and-store both PS4 and PS5 games. There's going to be lots of tough decisions on which games to keep or delete as the PS5 matures.