Here is Gigabyte Support CPU SUPPORT list. See which Processor listed you want to purchase. Also look at the BIOS version your Motherboard will need for the new processor to be recognized.
Here is the Ryzen 7 5700X and Ryzen 7 5800X and BIOS version needed to be installed: https://www.gigabyte.com/Motherboard/B550-AORUS-ELITE-rev-10/support#support-cpu
If you want to get a general idea if either of the above Ryzen CPUs will cause bottleneck with your RX 580 go to this FPS & BOTTLENECK website and input your data. It will show you if the CPU or GPU will bottleneck and by how much. IT will also show you various games with those CPUs and your GPU card: FPS & Bottleneck Calculator
NOTE: I inputted at the FPS & BOTTLENECK the following Data:
Ryzen 7 5800X, RX580, 16GB @3600Mz at 4k. This is what came up:
The above is just a general idea. But at 4K there isn't any significant Bottleneck to consider with the above hardware.
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