HDMI ports on game consoles fail for a simple reason: they're soldered directly to the motherboard and take a lot of force every time a cable is plugged in, pulled out, or yanked sideways by a kid tripping over it. Over time the pins bend or the solder joints crack, and the console keeps running with nothing on screen.
Rule out the easy stuff first. Try a different HDMI cable and a different input on the TV, and look into the port with a flashlight for bent pins or debris. If the picture flickers when you wiggle the cable, the port is almost certainly the problem.
Replacing the port means removing the old one from the board without lifting the pads, then soldering a new one in place. On the PS5 in particular, the port is fragile and the pads are small, so it's a job for a proper hot-air and microscope setup. If the pads are already damaged from a previous attempt, that's a board-level HDMI repair, which we also do.
PS5, PS4, Xbox Series X|S, Xbox One and Nintendo Switch are all handled at our bench, along with USB ports, fans, power supplies and power-on faults. Diagnostics are free, and you'll have a price before we open the case.