While it is now assumed that the DualShock 4 controller also works together with the PS5, this should also be possible the other way around.
Sony states on its own homepage that the DualShock 5 controller can also be used with the PS4 and PS4 Pro. However, this information can only be found on the PlayStation France website and not on other country-specific PlayStation websites.
So it remains to be seen whether it is a confirmed fact or a mistake on the part of Sony. This would not be surprising, since the transmission technology will probably be the same for the DualShock 4 and DualShock 5.
In this case, it would be exciting to know whether features such as the adaptive trigger and the haptic feedback can also be used on the PS4.
More information is expected at the speculated PlayStation 5 event in February.