It's going OT, only got 42 posts:S. Don't know why I used arch instead of well, it's just what popped in my head, ha ha.If you live in a hot climate and the car has done too for most of it's life there's a good chance the wheel arch liner plastic has become brittle and will crumble when you move it. Both my 540i and my 2002 M5 had this happen.
Good news is the pump is very cheap. item #3 in the list:
2002 BMW M5 Base Sedan - Wipers and Washers - Page 2
M5TX you've got PM as to not go OT on this thread.
OK, I found a few more useful thread and do see that the smaller, inner pump is for the windshield, and the larger outer one is for the headlights. I thought the intensive pump fed both.One pump for windshield and one for headlights. Check your fuse.