Sony says the DualShock 4 will work with the PS5 on select games
(Android Central)

Some extra clarification on what you`ll need. What you need to know Sony has issued new details on how PS4 accessories and controllers will work on PS5. The DualShock 4 controller will work on PS5 but only when playing PS4 games. PSVR accessories will work with PSVR titles on PS5. The PSVR will require an adapter to function on PS5. Sony has given out some new details on how PS4 accessories will work with the upcoming PS5. One of the biggest details is that you can use the DualShock 4 controller on the PS5 but only with backward compatible PS4 titles. The DualShock 4 cannot be used for new PS5 games, so you`ll have to have the DualSense in order to play titles like Horizon Forbidden West. Other officially licensed PS4 gamepads will be similarly compatible. The PlayStation Move and PlayStation VR Aim controllers will work with the PS5 and the PSVR was previously confirmed to work with PS5. The PSVR is going to require an adapter in order to work on PS5 however, this adaptor is ...