I'm pretty sure a 5850 is 151 watts. The PCI express slot supplies 75 watts, and a 6 pin PCI express connector supplies 75 watts. A better choice for your situation may be a 6850 which should be similarly priced with similar performance but uses about 30 watts less and only requires one PCI express 6 pin.
You may be ok with purchasing a molex adapter and using that for the second connector http://www.amazon.com/StarTech-com-6-Inch-Express-Adapter-LP4PCIEXADAP/dp/B0007RXDDM/ref=sr_1_1?ie=UTF8&qid=1321713329&sr=8-1
usually one or two of these will be included with a new card anyways.