No, video card manufacturers are infamous for overstating power supply requirements. Your existing power supply is adequate for the 7770 (or 7850, should you want even better gaming performance).
Note that the video card manufacturers are making recommendations for a "worst case" scenario like a power-hungry AMD eight-core CPU. However, the XPS 8500 has a power-sipping third-generation Intel "Core" CPU; if yours has an "Ivy Bridge" like a 3770, rest assured that 500 watts for the 7850 is overkill.