3 x used ATI 5870(gigabyte) = 3 cores +
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................................................9 cores
................Max cores per BIOS 8 cores -
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................................................1 cores too many for 1 mother board
5970 with 850/150 clocks draws 250watts each, x3=750watts.
5870 with 900/150 clocks draws 180watts each, x2=360watts.
........................................Motherboard draws about 160 watts.
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............................................................................... ...1270watts Too much for a 1200watt PSU
You should run 2x5970's and 3x5870's on your set up, but only if your PSU is designed to run at its rated capacity of 1200watts.
2x 750watt or 850watt single rail PSU's would be a better choice.
Your power estimate seems too high. I drew 1040W at the wall with 3 5970 and 2 5870 (all reference) with an 83% efficient PSU. This is about 863 watts. I believe it also did 2700 mhash, or 3.12 mhash/J (assuming 100% efficiency power supply)