It should be capable of running mid tier graphics cards, and it is an excellent budget PSU.I have the EVGA SuperNOVA 550 G3, 80 Plus Gold 550W. I only know what I given in the build by helper800
Make sure that your RAM is running at or near its advertised speed - that will help your 5600g's graphics run better. Run CPU-z and look at the "memory" tab. That will tell you what speed and timings your RAM is running. If you didn't configure your RAM in the BIOS then it might be running very slow - that will slow down your 5600g's graphics a lot. The 5600g needs fast system RAM because it uses system RAM as its video RAM.Nothing above $300
I would be comfortable putting any sub 250-300w GPU in that computer with that PSU.Would the GTX 980 or the GYX 970 that that larkspur mentioned be compatible with your build and if so, would I also need to upgrade my ram for the gpa?