"I just installed the AMD Radeon R9 280X 3GB (3 Fan) video card in my 2008 Mac Pro 3,1 (dual 2.8GHz) running Sierra 10.12.6 to run my 4K LG 32" Monitor. (LG 32UD59-B, nice monitor with adjustable height.) It works perfectly with no problems. I can get 3840 X 2160 @ 60HZ using SwitchResX, but I am running 2560 X 1440 @ 60HZ because of the scaling issues. (Menu bar text too small at 3840 X 2160.) I used a Mini DP to HDMI adapter from the card to my monitor on the 2008 Mac Pro. Really a nice easy update for an older Mac, that is still running great and giving me very good production.
The AMD Radeon R9 280X (2 fans) in my Mac Pro 2012 was purchased on eBay from MacMotive and it was flashed to be used on a Mac. The other is a Gigabyte AMD Radeon R9 280X (3 fans) that is in my 2008 Mac Pro, also purchased on eBay and flashed for the Mac.
I get the full start-up/login screen, even after sleep on the 2012 (MacPro 5,1 Dual 3.46GHz) and the 2008 Mac Pro (MacPro 3,1).
(I asked about the card's power connections, as Mac Pro has only two 6-pin connectors.)
The Radeon R9 280X 3GB cards come with 2 cables (6-pin & 8-pin) to mini 6-pin that plug in easily on the 2008-2012 Mac Pros.
I've ordered the Sapphire Pulse Radeon RX 580 8GB Card (for the Mac Pro 5,1), but have no idea when/if I will actually get it. (I found it for $340 (shipping included) from a seller in Texas on "Special Order", saying 4 to 6 weeks to deliver. The RX 580 8GB cards are hard to get right now and they are often over retail price.) The Sapphire Pulse Radeon RX 580 8GB or 4GB cards come with an 8-pin that needs a dual 6-pin splitter.
(Update: See his later report on a stock Pulse Radeon RX 580 8GB in his Mac Pro - it's the first report at bottom of linked page.)
The 2012 Mac Pro CineBench scores are 1620 CPU and 65 FPS. Geek Bench 4 is at 22,380 Multi-Core and 2933 Single. These are low. I've heard that it may be a RAM problem. If I lower my RAM from 64GB to 48GB, it may raise my Geek Bench scores. Don't know why.
(For 2009-2012 Mac Pros, the fastest memory bandwidth is with triple-channel memory configuration - 3 identical dimms per bank, vs 4. But in real-world use, more ram is a benefit for apps that use it.)
(He later wrote)
I went from 64GB of RAM to 32GB of RAM in the 2012 Mac Pro and increased my Geek Bench 4 score to Multi Score of 24,255 and Single Core of 2910. OpenCL Score - 107706. Go Figure. (There can be some variance from run/run. Similar scores with repeat runs from clean reboot? Benchmark doesn't need more RAM and slight overhead may be a factor if run/run variation isn't.)
My old Video Card was a Radeon 5770 1GB. No comparison to the Radeon R9 280X 3GB. The whole purpose was to be able to run a 4K Monitor, which this does with out a hitch at full resolution.