It turns out the result is just that both of the HDMI ports on this graphics card are busted. I just tried it on a whim with a DP cable and it works flawlessly, even with the 5600X.
I've been searching for a few days now and haven't found any advice that works.
I am building my own PC and have all my major components. Here they are:
CPU: AMD Ryzen 5 5600X
Mobo: AsRock B550M Pro4 mATX
RAM: Corsair LPX Vengeance 2x16Gb 3200mHz CL16
Storage: Samsung 980 PRO, 1tb
GPU: Gigabyte...