There is another thread where the OP experience bottleneck with his Athlon X2 6000+ and an HD5770. We can not find fault to these components and can only think that his motherboard with PCIe V1.0 is the only possible cause. But that is on an HD5770. Maybe the demands of the HD5670 will be less.
The HD5670 should play those games at those resolutions even at high settings. The new cards will work with PCIe V1.0 slots albeit with small ( or even no ) performance hits.
In fact, even your current 9500GT should be playing it as well but maybe a lower game setting. The only reason I can see you need a video card upgrade for is if you get a new monitor with a higher resolution say 1680x1050 and up.
But if you want to maximize your setting and see all graphic effects of the games, the HD5670 is good choice and should run with your current motherboard.