Here is the official ATI power recommendation for a pc system with an HD 5870 video card:
ATI Radeon™ HD5870 System Requirements:
PCI Express® based PC is required with one X16 lane graphics slot available on the motherboard.
500 Watt or greater power supply with two, 75 watt, 6-pin, PCI Express® power connectors.
600 Watt or greater power supply with four, 75 watt, 6-pin, PCI Express® connectors for ATI CrossFireX™ technology in dual mode.
The power supply recommendations are for an entire pc system.