AFAIK the Radeon 5800 uses a PCIe 2.1 x16 slot, so any newer PCIexpress card should fit although it may be limited by the constraints of your motherboard.
See here for more about the PCI express slots:
https://www.tomshardware.com/reviews...tion,5754.html
Depending on the motherboard, there may be an on-board graphics option as well. You could check for a different display connector on the back of your system. You may have to switch this in the BIOS though.