Recently, Sony announced that the current PlayStation 4 DualShock controllers won't be compatible with PlayStation 5 games... BUT they do go on to say that the PS4 controllers will work on the new system and will be supported by some PS4 digital titles, they are yet to release a compatibility list for the games
Sony said "We believe that PS5 games should take advantage of the new capabilities and features we’re bringing to the platform, including the features of the DualSense wireless controller"
Now as for accessories, they did state that racing wheels, flight sticks, the PlayStation Move motion controllers and VR Controllers will all work on the new console with supported games. When it comes to anything else that you currently use on your PS4's, we will have to wait and see if Sony is yet to confirm more accessories and support on the PlayStation 5.
Now we know the PS5 DualSense controller is packed with loads of features but this move is going to force consumers into buying an extra controller for more players. The Xbox, on the other hand, hasn't changed much and will continue to support the Xbox One controller on the upcoming Series X console.