Windows 7 - Will a good intel i3 or i5 increase fps a lot?

Hello, at the moment I have this:

Model: Packard Bell iXtreme M3720
Motherboard: MCP73PVT-PM
Processor: Intel Core 2 Quad CPU Q8300 @ 2.50GHz
Ram: 4GB
Graphics Card: Asus GeForce GTX 560 810MHz - (fully updated drivers)
Power Supply: OCZ 500w stealthxstream

and since i've had this new gtx 560 (previously had gt 240) I have seen a small fps increase in games such as Call of Duty Mw3, Bad Company 2, Battlefield 3, and Team Fortress 2. However smaller games such as Payday the Heist, CSS and Magicka have increased a lot.
What im asking is if I upgrade to a decent intel i3 or i5, will I see a big fps different.

Also to mention in BF3, no matter how low the graphics are the resolution, i still remain with the same fps. I can play on high settings and low settings and see no fps difference.

At the moment I get this FPS

MW3: 35fps - 60fps (rarely gets to 60) (Ran at 1600x900)
Battlefield 3: 25fps - 40fps (Ran at 1280x800)
Team Fortress 2: 35fps(in battle) to 80fps (no matter if maxed out or not) (Ran at 1600x900)

I feel the fps i get at the moment is extremely low for a gtx 560 and i was worried that my q8300 was bottlenecking but when i upgraded I was not expecting to see such as huge bottleneck and low fps in games.

Also sorry if i posted this in the wrong section.

"good Intel i3 or i5" covers a large range.

The fastest i5 probably has a general CPU benchmark 3 times as high as the slowest i3.

Maybe you can be more specific.

Im just wondering if its my Q8300 CPU which is bottlenecking me massively and wondering if upgrading to a decent i3 or i5 processor (cheap but fast would be nice) would significantly increase the fps I get at the moment.

I've got a slower processor than yourself and I don't see these slowdowns, same graphics card as well, name some of your games and i'll do a quick bench of them.

yes it will help speed up applications that involve heavy 3d graphics, noticeably

I say go with a i5 there about 200usd and they are quad cores get it with a frequency around 2.5-3.0

It will help you in FPS but in mostly in those games which are CPU Intensive Titles.... Lets say i.e. GTA IV

battlefield 3, bad company 2, black ops, mw3, tf2 or l4d2. Any of them would be nice to know.

Also someone recommended me to do a driver wipe, is that recommended?

of your system specs, BF3 & MW3 fps is so drop ... i guess there's something wrong with your system setting as a whole or just a graphic driver issue. Upgrading cpu can increase fps but not as much increase as when it's a cpu demanding games like gta iv.

it will help you in black ops, black ops is a bit cpu intensive