I am not familiar with BM53 part number 65.12-4 135 562. Here is a pretty good post that lists the known part numbers and when they got certain features. the -562 number does not show up on this list, so I have no idea what it is.
Thanks again Roy. To consolidate ur recent posts...

Yes, that Sirius receiver module will work.

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SOLD
2000 E38 750iL Highline Edition, Upgraded with the lastest 2006 X5 Electronics
MKIV Navigation, 16:9 Display, Bluetooth, TV/Video with Backup Camera, Sirius, and Aux Input