I suspect nobody is replying because it would be easy enough for you to either open your case and check for the connector, or link to the product page or a review online where we could see this info.
Similarly you can look up the TDP of the RX5800, divide that by 12 since it runs off the 12V rail, then see how many amps the PSU has available on its video card connector or if shared 12V rails, how many amps total compared to the sum of the video card plus the rest of the system.
However you wrote cardS, plural. If you mean more than one card you would obviously need to double the amperage allowance.
If your PSU is the old Silencer 610 model, it appears to have a single, 49A, 12V rail. RX580 video card has a TDP of about 185W which divided by 12 is 15.4A, subtracted from 49A, yes if the rest of your system is typical then your PSU is adequate for a single RX580, possibly two of them but it would be a lot closer to its limits.
On the other hand, some people would advise you not to risk a system on a 10 year old PSU, that it is old enough that it is due to be retired. Personally, I like to run equipment as long as I can and would use it but only after checking the fan for smooth operation and cleaning the dust out and while open, examining it for burst capacitors and not using it if any are failing.