Is the PS5 connected to a different HDMI port? If yes, the port may have its own settings (brightness etc.) that differ from the port the PS4 is connected to. Try to match the PS4 port's settings or use the previous port without changing any of its settings to see if it helps.
I only have a (usable) PS4 but I made sure to disable HDR. Being sensitive to high LED brightness, I need to have full control over the brightness, and HDR would take that away.
Also try to analyze if the eye strain comes from particular games. Some games on the PS4 are sources of eye strain for me. It has been the same for the PS3.