Although there are no official confirmations yet, it appears that the current DualShock 4 will be perfectly compatible with PlayStation 5, at least judging by reports from some developers working on games for the new Sony console.
In particular, an anonymous developer would have confirmed to RespawnFirst the full compatibility of the DualShock 4 with the PS5 development kit he used, as revealed also by a photo that you find at the bottom of the news. In addition, many have noted how the controller is in the DualShock 5 patents filed by Sony represented graphically in a very similar way to the current PlayStation 4 joypad.
This does not mean of course that Sony will not present a DualShock 5, the new controller has recently been at the center of leak on the keys and functionality of the same, the DualShock 4 in any case can also be used on the new console exactly as it will happen with the Xbox Wireless Controller and Elite Controller on the Xbox Series X.
Sony announced the Back Button Attachment for the DualShock 4 in December, an accessory that could therefore also come in handy from a PlayStation 5 perspective. Sony also seems to have chosen the path of total compatibility with peripherals and accessories already on the market to make the passage between the two platforms less traumatic.