I was a huge PPC fan back in the day. But to be using a system that is so old and slow is a bit laughable. Even a base dual core pentium is most likely close to a dual socket G5 while using about 1/10th the power.
But back on topic, PPC GPU's ran a different BIOS than X86 cards. Yes you can physically insert a non-apple BIOS card (Some require trimming some pins), and it will display an image, but there will be no hardware acceleration or in some cases no image at all. Now some cards you can flash with the Apple BIOS, but this only works for some cards.
Since the 6950 came out long after your G5 did, you are most likely completely out of luck.
EDIT: Oh yeah, AMD has no modern GPU drivers for PPC linux last I checked. Only x86 Linux.