adampc18: And The HD 5670 graphics card should have no problem fitting in the casing right?
I'm going to take a wild guess, based on your specs, that you got one of the HP Pavilions that Wal-Mart and Fry's sell (P6523W or something like that).
Those HPs have a full-width case, a motherboard with a PCI-Express x16 slot, plenty of clearance even for larger cards, and a 250W power supply.
The power supply is the major concern. I would probably not tax it with even a 5670; I would go down a step to the 5570, which draws only 39W at full load. The 5570 is just an underclocked 5670, and it should be OK at low settings.
If you have money for both a power supply and a new graphics card, of course, the sky's the limit (but I wouldn't unbalance your system by putting, say, an HD 5850 with that Athlon II x2).