The bulb is an LED so it's pretty unlikely the bulb is the problem. As mentioned above, if the door panel was removed (for say a regulator) the little thin light tube that the bulb is mounted on most likely got snapped. Easy fix, pull the door panel and... some super glue will fix you right up.

__________________
2005 X5 4.4i Build 04/05 Maintenance/Build Log
Nav, Pano, Sport (Purchased 06/14 w/ 109,000 miles) (Sold 8/15 w/121,000 miles)

2006 X5 4.8is Build 11/05 Maintenance/Build Log
Nav, DSP, Pano, Running Boards, OEM Tow Hitch, Cold Weather Pckg (Purchased 08/15 w/ 90,500 miles)

2010 X5 35d Build 02/10
Nav, HiFi, 6 DVD, Sports Pckg, Cold Weather Pckg, HUD, CAS, Running Boards, Leather Dash, PDC, Pano (Purchased 03/17 w/ 136,120 miles)