Hi Salemyang, The hands of your watch have been fitted incorrectly. This is evident from your observation-"the hands align when you use the crown to set the watch, but when you let it run naturally, the alignment will always be off" Compared with an average watch, the movement in your 5001 has a greater number of wheels involved with dividing and transmiting the power from the train to the motion work(The wheels to which the hands ar fitted). There has to be a small ammount of play between the teeth of each of these wheels for the correct functioning of the watch but this small ammount multiplied by numerous wheels can result in a 2 or 3 minute difference in the time, indicated by the minute hand, between power coming from the crown and power coming from the train. The watchmaker fitting your hands fitted the hour hand,turned the hands clockwise to 12 and fitted the minute hand(as is standard procedure with less complicated watches). To eliminate your problem, the hour hand should be fitted,the hands turned anti-clockwise to 12 and then the minute hand fitted. Leo
And that explanation by Leo is the first explanation I have seen on the subject from an expert rather than someone who thinks they are an expert! The previous posts got me worried re my own 5001 but I have no such issues on my watch, either before servicing or after servicing by the UK servicing department of which Leo is the service manager.
Thank you very much for the update Leo. My 5001 also had a misalignment but it was not too big so I just let it be, probably something to mention at a regular service.