Thanks for the reply Mosox. My top priority right now is stability. The recommended power for the HD 5750 is 500W, which seems to be overkill for my 350 W PSU. I don't really wish to risk frying another video card.
Considering my PSU, my safest option is the NVidia GT240 DDR5, which only requires 300W. The HD 5670 seems to be the superior card though. In view of this, do you recommend I stick with the HD 5670? How reliable do you think it's going to be with my PSU?
It should run fine unless your PSU is a POS and fluctuates when it's under half load. Those Lite-On PSUs are cheap, but they are usually pretty decent so I say just try it and chances are it will be fine. If you have any stability issues, then you may have to look at your PSU.