what opsys and 32 or 64bit...and do you own the disc ? monitor and resolution........ the graphics card is probably killing you.........
at this point in time i wouldn't put lipstick on a pig......... no insult meant, but, you're not going to gain much of anything going to a 965. AMD's processors have been lagging over the past 4 years or so and even a mediocre Intel has faster through put.
skyrim is gpu limited more than cpu limited. you need to do more research. and last time I looked ati had bigger problems keeping up in that game for whatever reason. spit/sputter/lag.
think about an Intel 2500 or 2500k build with one of those cards you listed above.