Apple has an "official" list of graphics cards that are compatible with the Mac Pros (Mid 2010).
The ones specific to the 5,1 are:
Mac Pro (Mid 2010) and Mac Pro (Mid 2012)
- ATI Radeon HD 5770
- ATI Radeon HD 5870
Now, according to EveryMac.com, there are several more adapters that are compatible:
Please note that the Sapphire Radeon HD 7950 only is compatible with
the "Mid-2010" and "Mid-2012" Mac Pro models. The other four video
cards above are compatible with the "Early 2008" and "Early 2009" as
well as the "Mid-2010" and "Mid-2012" Mac Pro models.
Personally, I have used the AMD Sapphire Radeon HD 7950 because it wasn't just compatible with OS X (10.7+), but Windows Vista (which meant it worked in 7 and should work in Windows 10) and FreeBSD as well.
I am currently refurbing a Mid-2012 Mac Pro (side project) and I fully intend to put this exact card in the mix.