If your car is an auto then it might be the infamous gearbox whine. Mine used to do it a lot when cold but once things had warmed up it was fine. If it's autobox whine then it's probably low transmission fluid and/or a blocked filter - do you know if the fluid and filter have ever been changed? For more info, do a search (Google is good as there lots of info on the www.e38 forum, not just this one) for "5HP30" (which is the model number of the gearbox) and "whine".