Backwards compatibility with the PlayStation 5 will be restricted to PS4 games only, and even then, you'll not necessarily get all of them. According to Ubisoft, Sony won't be able to support games from earlier generations of PlayStation consoles, outside of emulation. Their hardware was just too different to work on modern systems like the PS5.
"Backwards compatibility will be available for supported PlayStation 4 titles, but will not be possible for PlayStation 3, PlayStation 2, or PlayStation games," Ubisoft claims on its support page (via Kotaku).
Backwards compatibility is an important components of a new console, as it massively increases its game library on launch day. While the catalog of new games can be built up, it helps to have a collection of older games that can be enjoyed by new and old gamers alike. The PS5 will support a lot of PS4 games right out of the gate, but don't expect to bring your PS3 collection along for the ride also.
This is a stark difference to what we expect to see on the Xbox Series X. Microsoft has recently promised that it would bring games from the original Xbox, Xbox 360, and Xbox One libraries to the Series X, potentially leading to a game library that is thousands strong right from the get go.
Would that tempt you to buy a new Xbox over a new PlayStation?