asus p5ld2-x/gbl mainboard
e4600 core 2 duo 2.4ghz cpu
2 gb ddr 667 ram
Codegen MX400 400W psu
this system support 5770 or 5750
if not i will buy hd5670
I wouldn't trust using an HD57xx with an unknown brand PSU. Also, the HD5750 requires a 450W PSU as per AMD's website (and even then, it still depends on the amperage of your +12V rail).
So if you really want to be on the safe-side, you should buy a better PSU (Seasonic, Antec, OCZ, Corsair, Coolermaster...).
Or if you want to risk it, the HD5670 MIGHT
Always remember, the PSU is the most important part on your computer. Everything else's safety depends on it.