HDMI port is damaged

I would not recommend doing this yourself if you do not have any experience with soldering. I would take it to a repair shop near you.

First, what you would want do do is follow a teardown guide or video for the PS5 Slim. You can find this on Google. After you have succeeded in taking out the motherboard, prop the board up on non-conductive materials. Make sure that it won't wobble or move easily. Take a heat gun and focus it on the underside of the board where the HDMI port is. Grab the port with tweezers and without yanking, slowly wiggle out the heated port. If the old solder bubbles are on the board, then take your replacement and put it where the old one was. If there aren't, then put the port in and solder all of the contacts to each other. Finally, put the PS5 Slim back together by reversing your way through the teardown guide.