This is the main drive belt (serpentine belt) for the M62 and S62 engines in the E39 540i/M5, E38 740i/740iL, and E31 840ci. The main drive belt runs the water pump, power steering pump, and the alternator and is not something you want to skip on any maintenance routine. The size is 7K1629 and it's made by ContiTech, the original supplier to BMW for drive belts.
If you are replacing your belts as part of a preventative maintenance plan, also consider replacing the pulley and belt tensioner. You can inspect these for wear or fatigue and order everything you need together. Plastic parts such as pulleys tend to crack with age so staying on top of maintenance will avoid a much bigger repair bill later on.
BMW Fitments:
5 Series
E39 (97-03) > 540i
E39 (97-03) > M5 (00-03)
7 Series
E38 (95-01) > 740i
E38 (95-01) > 740iL
8 Series
E31 (91-97) > 840Ci