I measured at wall (via Kill-A-Watt) a cheap non-IGP MB loaded with a Sempron 140, 2GB DDR3, 2.5" SATA and a simple PCI video card at a little under 70W with CPU running at full load, no load at about 52W.

An 85% efficient 850W would give ~722W to play with, minus 70W for system leaves ~652W for GPUs. ~652W/4 = 163W per GPU available.

I would be safe and go for a 1KW PSU if at all possible. 163W per 5870 GPU is cutting it mighty close IMO unless you do some aggressive underclocking/undervolting.