That is your Board Monitor radio module. You can get a new one from Crevier BMW for around $450. They occasionally show up on eBay and sell for around $350, so I would vote to get a new one.

You do not have to worry about replacing your exact part number. You can use your PN or anything newer. Here is a list of the radio part numbers I know about that would work in your car. The first one in the list is the newest PN that I know about. The cool thing is that if you get the any radio -910 or newer, it will support Sirius. The -961 fully radio supports MP3 if you get the newer BMW X5 CD changer that supports MP3 disks.

65.12-6 976 961 (or 962)
65.12-6 972 664 (or 665)
65.12-6 964 398 (or 399)
65.12-6 943 449 (or 450)
65.12-6 927 910 (or 911)
65.10-6 933 089 (or 090)
65.12-6 922 512 (or 513)
65.12-6 919 080 (or 081)
65.12-6 904 213 (or 214)

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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