Upgrading motherboard and CPU

Hi.
I am planning to change my motherboard and CPU. At first I thought only to change the processor but Intel processors are so expensive. So now i'm planning to buy AMD.

My computer specs are given below. I wont be changing my graphics card. Or RAM. Only the CPU and mobo.And the PSU.
So these are the models i have selected:

AMD 3.5 AM3+ FX4300 or FX6300 Processor
ASUS M5A78L-M USB3 Motherboard.

My query is whether i should buy a 4 core or 6 core processor, considering my graphics card is not so great. Will the GPU hold back my CPU?
My graphics is NVIDIA GeForce GT 610 2GB synergy edition.

I would be grateful for any input. Thank you.
Preethy.

PS. I use my pc for gaming.

fireberd said:

I would give the memory some thought. Is the memory certified by ASUS for the motherboard (they have a list of certified memory)? Is the memory speed right? Slow memory and your CPU/Motherboard upgrade may be bottlenecked by the memory.

ASUS Memory List

The 5GB you list may not be adequate for gaming and you should change to 64 bit OS.

Thank you for the reply.

Sorry. I forgot to update my system specs. I upgraded to 64 bit OS a while ago.