In this case...the part you're asking help about is a universal part...but it helps us to help you better when we have model/model year/build date information. Most members create a signature that contains this information...or they provide it in their car info that appears in the upper right of their posts.
This helps us when we need to look up parts/diagrams etc...or make suggestions/recommendations or answers that are specific to the multiple engines, transmissions, and options that occur through the production range from 2000-2006.
In this case, your local BMW dealership's parts dept would know exactly which part to order, since they can order a lock cylinder based specifically on your car's VIN...the cylinder will come in made specifically to fit your key's cut.
You need #11 in the diagram below...make sure you explain to the parts counter clerk (or have them explain to you) which one you need to order (there's 2 choices)...the link below is based on my 06 4.4 X5 since there was no model/model yr/build date info to embed a direct link to the part database based on the e53 you own: