Update Bios if changing from 8600GT to HD 5850

No you should not need to --- the PCI-e interface and OS already handle communication with the video card and the BIOS has nothing to do with that that will be affected by changing video cards. (the only time a BIOS update would be needed is if there was some problem in the BIOS that kept the PCI-e interfaace from working properly but then you'd have already had problems using the 8600GT.)