
While Sony has maintained a list of PS4 games that are not playable on the PS5 through backward compatibility, others that are playable can lead to weird glitches.

Assassin's Creed Syndicate recently got a 60 FPS update, allowing the game to run at 4K and 60 FPS on PS5, PS5 Pro, and Xbox Series S|X.
It is amazing what's available. Blue Dragon. Binary Domain. AVP. Chaos Theory. Lots of gems to be had.
There is no re-start option (that I can find). Since I've already finished the story years ago, I can't re-start it to check the new update.

Revisit the Assassin fantasy and take down your enemies more smoothly than ever on Assassin's Creed Syndicate’s free 60 FPS patch.
AC Unity next Please! despite the technical issues it was a good game even though it was too ambitious for PS4 and Xbox One the graphics hold up well. I would love to see it on PS5 and Xbox Series Consoles
Is Syndicate any good? I own them all since they end up in the bargain bin but I haven’t played one through since Black Flag
If you've read my comments here before, you know damn well that I'm always quick to mock Ubisoft, but in this case, its good news. Glad to see that Syndicate went from being almost broken on PS5 BC, to receiving a free 60 FPS update patch.
While this game did have grind elements, and skill trees, it wasn't exhaustively grindy like the later games would end up being. The London setting was amazing, too, and the soundtrack by Austin Wintory was fantastic. I really liked playing as a brother and sister duo as well.
It was a good game, and the last one in the series I truly enjoyed.
Why are the patch sizes so different between Xbox Series and PlayStation 5? Its a 35 GBs difference.
Patch notes:
Xbox (~31.8 GB)
Xbox Series X
4K resolution at 60 fps
Xbox Series S
1080p resolution at 60 fps
PlayStation (~0.75 GB)
PS5 and PS5 Pro
1080p resolution at 60 fps
4K resolution at 60 fps

Assassin's Creed Syndicate is free on PC when you have a Ubisoft Connect account until December 6th, 2023.
I loved Syndicate! I played this game mostly as Evie because of her stealth abilities and loved using a cane sword.
Hopefully Sony releases a BC patch at some point to increase stability across all games.
I've noticed a lighting glitch (flashy sun light on buildings) while playing the Ezio Collection on PS4, so I'm not surprised Syndicate is even worse on PS5.
Bare in mind the PS5 isn't even properly released yet so I'm sure a lot of stuff will be addressed in future patches.
I hope they fix Assassin's Creed Syndicate. It's probably the only game I would maybe play via backwards compatibility, that doesn't seem to work correctly. All the other games Sony listed that won't work, I don't own, or never even heard of.
So if I plug my external hdd full of PS4 games into my ps5 does it play those games directly off of the hdd or do I need to transfer them to the ps5 system before I can play them?