I also was not able to get the Solarflare 10GbE Ethernet card that had worked fine in High Sierra to work at all in Catalina, so I ordered an Aquantia AQC107-based card. The TDP of the 5700 XT is 225-watts, and therefore presents no special challenges to the factory power capabilities of the 5,1 Mac Pro. The PowerColor 5700 XT version that I have uses a 6-pin and an 8-pin power connector, so you'll need mini-PCIe power cables of each. Now that I have a separate Win10 machine, I *hope* that I can get along without using the option key to go between OS boots simply sliding in the boot SSD that I want. I 'needed' the flashed video card when I routinely went back-and-forth between Win10 and macOS. It now has a normal (un-flashed) Radeon 5700 XT.
It had been at High Sierra with a flashed Nvidia GTX 1070. Just two days ago, I was able to get Catalina working in my 12-core 2010 Mac Pro.
