Hi dude. Welcome to the forum. E39 is king.
Some bad news for you - this is not a 2003. It's a pre-facelift so it would be a 2000 or older year model.
You can tell this by the front fog lights, they are squared whereas facelifted models 2001-2003 were rounded. The kidney grills have a sunken-in look rather than a broader extruded chrome border of the facelift. The centre armrest with the phone was mostly replaced by either a plain flat armrest or the phone was just not there, leaving a large storage area in the lid instead.
It has facelift tail lights (clear indicators) and aftermarket headlights. It also has M5 side mirrors.
While it's definitely an M-sport, it's not a 2003 and I hope you weren't duped into thinking it is by whoever sold it to you.
Edit: also she's a manual, and manual E39 540i's are rare. Restore her, keep her, and look after her.