As Bouke and Shane stated, your machine is not a G5.
It sounds like you have a have an early Mac Pro. This Mac Pro will run MC 4 and will even run MC 6 ( however it will be unsupported, as if I have your machine correctly identified, it will not boot the 64 bit kernel)
As stated, check the matrix on Avids website to determine the optimal OS for your version of Avid.
Avid supports any graphics card supported for your Mac.
You should seriously upgrade your RAM. 4 GB is way to little. I have 32GB in a similar machine, but you don't need to max it out like I did,