you have two 12 volt rails
One is 14 Amps
The other is 13 Amps
The EVGA 560 Ti needs 30 Ampshttp://www.evga.com/products/moreInfo.asp?pn=01G-P3-1563-AR
You only have 27 Amps... So no it won't work.
Your PSU rates 500 Watts because much of the wattage is dedicated to the 3.3V and 5V rails. Usually this indicates a poor quality build as it is inexpensive to put the power where it is generally not needed.