As for jacking the car up, the E39 is a bit squirrelly. The jacking points that you need to use are located directly under the engine bay, in a very hard to reach location:
And the rear jacking point is basically the rear differential.
So, I drove the car up on some make-shift (yet stable) ramps and jacked the front up and went straight to work.
Take off the wheels once up on jack stands (located near each wheel, towards the center of the body) and this is what you see.
What you are going to take off first is the rattle clip. Take it off carefully, as it might fly anywhere if you don't. I like to keep a hand on the front of it so it doesn't get away from me and jettison towards my camera girl (which it did, even with my hand on it).