The quality of rebuilt alternator at local parts store is just terrible. The rebuilders do a bare bone minimum, sometimes not replacing bearing, VR at all.
You have 2 options:
1. Rebuild it the proper way. If Valeo, DIY for E39 is below, E53 almost the same:
Diy: Valeo alternator rebuild - Bimmerfest - BMW Forums
If you have a Bosch unit, then search bimmerfest E39 for info.
2. Buy NEW.
- Although not formally listed, the Bosch AL0703N fits both M52 and M54 engines.
About $235 at eeuroparts dot com.
- Valeo (12317501599).
Given that rebuilt is so bad and you can get stranded in the middle of nowhere, I'd go for
new Valeo. In the big scheme of things, it is not expensive for something that lasts 150K+.
Valeo 12317501599 is about $300 at rmeuropean dot com.