7850 uses a 6-pin and the PCIe lane as power imputs, so that (if i recall correctly) sums up to a MAXIMUM power draw of 150+75 (6-pin + pci) so I'd say you are pretty much on the limit there. Remember that wattage is not that important, the important part is the Amps that the 12v rail (preferently, a single 12v rail, avoid multiple) can deliver. A good 480w power supply should be able to deliver about 420w efficiently, so try not to overdue it.
If you dont know anything about efficiency or actual power being delivered by your PSU, it may be a good idea to buy a new one, not for the watts, but for the reliability. Usually those OEM systems use really crappy power supplies.
Im not an expert though, wait for further comments c: