More aboutwhat highest graphic card computer support
If you remove a drive bracket, your case will support GPUs up to 422mm/16.6 inches in length. That being the case, you could install either a Radeon HD7970 or Nvidia GTX680/690. That is from a space stand-point.
While I am not familiar with Gigabyte PSUs, the company generally makes good products. At 500W. I would stick to a Radeon 7950 or GTX 670.
But I would surely recommend you a better PSU, as you have No Limit And btw which model i5 it is?
In that case I would agree with COLGeek. I also am not familiar with the Gigabyte powersupplies. Haven't seen any reviews of them. The company does make good products so I would hope they made a decent power supply. 500W is limiting though so his suggestion of a 7950 or GTX 670 is spot on. Make sure you have the spare power connector for the card off your power supply before ordering.