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you can overclock just fine. I have 2 5870's, 1 is a stock sapphire, and one is a asus rom'd MSI. When i go into CCC and go and enable ATI overdrive, there is a drop down that lets me pick each card, and I can set the overclock differently on both cards.
funny thing is my card w/ the asus rom allows me to go up to 1400 core clock, and 1500 memory where the stock sapphire limits me to 900 and 1300.
i can overclock both though, and I would assume you could do the same with the 5850, and would be limited to the clocks the 5850 bios allows.