Ubisoft has revealed via their support page that the PS5 will not be backwards compatible with PS3, PS2, or PS1 games.
The page which information PS5 players having the ability to play online multiplayer games mentions the following:
PlayStation 4 players will have the ability to join multiplayer games with PlayStation 5 players.
Backwards compatibility will be available for supported PlayStation 4 titles, however will not be possible for PlayStation 3, PlayStation 2, or PlayStation games.
This isn’t completely surprising as Sony have not pointed out any kind of backwards compatibility for consoles besides the PS4, however it is great to lastly get confirmation from an official source, instead of reports and speculation.