Here are the official power requirements for the ATI Radeon HD 5850 and HD 5870 video cards.
ATI Radeon™ HD5850 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® power connectors for ATI CrossFireX™ technology in dual mode.
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
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For a pc system with one HD 5870 or one HD 5850 video card the OCZ Z series 550 watt power supply will be okay!