PlayStation 5 will be backwards compatible with PS4 games. This we know, but to exactly what extent has been kind of up in the air. The hope is that all your current-gen software will run as expected on the PS5, but Sony has yet to officially confirm how far the console's backwards compatibility will stretch. In a new quote from Ubisoft, it sounds like Sony will have almost everything ready to go.
During a financial call, the publisher's head honcho, Yves Guillemot, answered a question regarding next-gen systems and backwards compatibility. "Those consoles will be running almost all the back catalog of the previous consoles," he said. "It will be something new in the industry. It will help the old generations to continue to be big consoles on the market for years to come."
It's an interesting quote, and suggests that the PS5 will play almost every PS4 title. However, there's definitely some wiggle room in his words. You could, for example, read into his statement that PS5 could run PS3, PS2, and PSone games too -- "the old generations", if you will. This is pure speculation, obviously, but given he hasn't specified machines, it could mean anything. Odds are he's simply talking about PS5 and Xbox Series X being backwards compatible with PS4 and Xbox One, though.
Whatever the case, it sounds like PS5 will be able to play pretty much your entire PS4 library. Hopefully Sony will tell us more about its next-gen plans soon.