i want to buy an Sapphire AMD/ATI Radeon R7 265 DUAL-X 2GB Graphics Card
will my Intel Core i3 540 cpu hold the graphics card back
motherboard - dh55tc
ram - 3 sticks of ddr3 2gb ram
I don't see why it would in most games, here is a comparison to the Athlon X4 760K which is a very popular choice for mid-range gaming LINK
Here is a video of someone using the i3-540 and 7850 (R7 265) to play Crisis 3 beta and the combination seems very promising. LINK
I think it should work fine for most games.