It depends on the quality of your 500W PSU. If it is some off brand, no-name, cheapie, over-rated at 500W, it may not be able to maintain the voltage during heavy gaming when the card is stressed. That's when the card will be at its highest demand. The HD 7850 demands 130W at max. That relates to ~10.8A on the +12V rail. Check your PSU's nameplate and see what its +12V rail(s) is rated at in amps.
What is the make and model of your PSU? Good quality 500W PSUs will have no problem with that card or bigger.