There are 24 part nbrs at this link:
Single parts SA 639, trunk | BMW X5 E53 X5 4.4i N62 USA
All of them are listed as (
#1)...some are no longer available (new) but are out there in the used market...but all will work for e53 owners. Shop for a BMW TCU using ANY of those 24 part nbrs...and it will give you results for a TCU that is plug-n-play.
TCUs with a build date printed on them prior to 10/04...will probably not have what you need. And if you shop for a TCU from a new gen BMW (like an e60/e65/e70/e71/etc)...they may not be compatible since they were designed to communicate on the (I believe) MOST bus which our e53s do NOT have.
I can't verify if the TCUs designed for the new gen BMWs will work (someone please chime in if you know for sure)...but with the ability to quickly find out which BMW models are listed for a part nbr using the database...I'd personally stick with the multitude of part nbrs listed as being compatible and exchangeable for the e53.
Good luck.
