A 5770 isn't really all that much better than a 4850. Performance-wise, the two are similar. Much like the difference between the 4850 and a 4870. A 4850 should be ripping through most games at that resolution.
Yes, your Phenom 9650 is a quad. But, the original Phenoms are not all that great. They're firmly set on the slow side as far as actual clock speeds are concerned, and their performance has never been close to cutting-edge. As mentioned, you could try overclocking it, but with stock cooling, I doubt you'll see much headroom.
Of course, we don't know what games you're talking about, what drivers are installed, and numerous other variables that could be contributing factors to your less than expected results.
Main thing that your processor lacks is clock speed.It is just 2.13Ghz which is way too low for modern games.
PhenomI series were terrible overclockers.
So better upgrade your CPU if you want better gaming performance.
Get this Athlon x3 440 processor with this mobo.That will be a good upgrade