yes you are no doubt bottle necked a bit with that cpu, I have a backup rig running an Athlon II 240 Regor 2.8 GHz stock and a 5770 and I have it oc'ed to 3.5ghz and it gives a big performance boost to the 5770, id say pick up a cheap aftermarket cooler and try to oc you CPU to at least 3.2 or more..
also you ram speed may hold you back if you are not running it at least 667mhz and even that is slow as hell you should try to get you ram to run as ddr 2 800 and overclock that CPU and you should be good to go, otherwise I'd say you will be held back to a certain extent. Although with 6 gigs you should be fine it is just odd that it is running at such a low speed to me.
Hooru: your 965 is worlds better than the chip the OP has so naturally your 5770 should run to its full capability. Furthermore crysis 2 is a bad game to gauge performance with imo bc it is dx9 crap, sorry to shoot that game down but a much better bench would be BFBC2 because of its dx11 utilization and graphical prowess alone.
Just Cause 2 is a good one to really stress the gpu while only utilizing 2 cores.
OP: that is my 2 cents, good luck and have fun.
Feel free to PM me if you have any further questions regarding this rig.