I have X5675 on P6TD Deluxe X58 mobo and reference Sapphire RX 5700 (flashed to 5700 XTX 50th Anniversary), had same issue, card can boot into bios, but after post it shows black screen if you try to boot something (windows, flash drive, dos, etc)
I know that is works on my i7-930 too.
It should work on P6T Deluxe, P6T WS, P6T WS PRO, P6X58D Premium too.
Got it working just by ENABLING Express Gate, if it is disabled card will show black screen after bios post ends. I boot to windows on ADATA SX8200 nvme ssd from refind efi bootloader.
I removed all contents of Express Gate flash drive so it just show loading screen for 1-2 seconds and pass to the bios.
I have x58 rev b2 (13 in cpu-z)
If you have Express Gate feature, then turn it on.
If you can't, try to attach another card to 1st PCI-E slot. Something like GT 210, use it as primary VGA. RX 5700 should work if you can pass into Windows. Then you can turn off second VGA in device manager and Windows will work with only one VGA.
sorry for my English
