PS5 DualSense controller is compatible with PS3, not PS4 - MSPoweruser
For those that don't want to use the Dualshock3/SixAxis - I highly recommend the Brook Wingman XE. I love the PS3, but the experience is just another level with the Dualsense IMO. :
PS5's DualSense controller works with PS3, but not PS4 | VGC
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PS5 DualSense Controller Works With PS3 Consoles
PS5 Controller on PS3 - the PS4 Can't Do This with the Dualsense Yet - YouTube
Having a blast replaying RDR with a dualsense : r/PS3
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PS5 DualSense Controller Reportedly Works On PS3, For Some Reason