I have the same CPU, motherboard, 4gb of RAM and a GPU that is somewhat the AMD equivalent, the 560TI should be slightly better. I've completed Crysis (the first one) with everything on Very High minus 3 or 4 things that were on High, with an average 40-50 fps. As for every other game I've played, everything runs smooth at 60fps with all graphical settings set to the bare maximum. Games such as Batman: Arkham Asylum, Spiderman Shattered Dimensions, Mirror's Edge, TF2, L4D2, at least that's what I've tried so far.
If you're gonna get a 550w power supply, make sure you get a good one, I have a XFX Pro Core Edition 550W power supply, the 12V rail is enough to power everything up. I'd recommend an equally good 600w power supply or above for the GPU you mentioned. I'd rather get the PSU I own compared to a cheap 600W PSU though.