Malthcom is correct, it could simply be a touch low on refrigerant. I had a Tahoe a few years back that needed almost exactly a pound every spring. Over the winter it would leak just enough so the compressor wouldn't kick.

Bulks method will work too, I've done that in the past, but in a different manner. Truck running, make a little jumper wire, pull the electrical connection, bridge it, and trick the compressor into engaging the clutch.

I will give the same disclaimer tho: I've never done it on an E53, or any Bimmer for that matter. It could cause the moon to crash into the Earth in a horrible catastrophe. Or the Sun could burn out. Or every pixel in every Bimmer on the planet could stop working.