Yes, there is a driver available directly from AMD, their drag-n-drop video recoder that uses the GPU. It should work great on your 5850:
AMD Media Codec Package (Previously known as the Avivo(TM) Package)
http://support.amd.com/us/gpudownload/windows/Pages/eyespeed_downloads.aspx
It's in CCC under video
Don't even bother with the CCC integrated video encoder, it's absolute garbage.
You're much better-off with being patient and using x264/Handbrake.
Media coder x64 is free and should work in tandem with your gpu/cpu, best GPU encoding app I've found to date. Bit rate is everything as far as quality goes, GPU's make for some terrible picture quality at lower bit rates but at higher bit rates you'd be hard pressed to notice a difference from a CPU encode.
A single GPU won't be any faster than your i7 though.