Maybe you can try connecting to the different ports of your Sapphire RX580. There's another MR thread here as the user is getting a black screen issue on his 2009 Mac Pro with Sapphire RX580
Mac Pro 2009 Sapphire Pulse Radeon RX 580 Display Issue
OK So ... I was gifted a: Mac Pro (Early 2009) 2.66 GHz Quad-Core Intel Xeon 8GB DDR3 I flashed the BIOS from 4,1 to 5,1 without any issues and then I upgraded to macOS High Sierra (Version 10.13.6) Still no issues. My new Graphics Card showed up: (Sapphire Pulse Radeon RX 580 8GB and the...forums.macrumors.com
I will try again the other ports, currently I’m trying only the dvi