I bought this E53 with only one key, its remote function inop. I assumed it was dead, and not having a spare makes me nervous, so I ordered a new key at BMW in Deutschland. The price was €150 (about £120) which seems fair.

Time to program the new key to the car, eh? www.obdii365.com technician and others have it though. Here it is just in case anybody else needs it. So the next time somebody searches here they can find this.

It worked like a charm, and as an added bonus, the key that came with our car also coded up just fine. So now I have two fully-functional keys. Life is good.

PROCEDURE TO FOLLOW:

1. Get into the car. Close all doors.
2. Insert new key into ignition.
3. Turn one click to the right, then turn it back, within 5 seconds.
4. Remove the ignition key and hold it so you can push its buttons.
5. Press unlock button and hold. Don't let go until step 7.
6. Within 10 seconds press and release the lock button three times.
7. Release unlock button.
8. LED flashes slowly for 10 seconds (some models).
9. Central locking system locks and unlocks (some models).
10. Step 8 or 9 indicate correct programming.
11. Repeat the above if step 8 or 9 don't happen or LED keeps flashing.
12. Re-code your other keys quickly now (see below).

NOTE: There is a maximum of 4 programmable keys allowed.
Any other keys will need to be re-coded too now (but they will still start the car!)
Perform programming of each subsequent key within 30 seconds.

See https://www.bmwgm5.com/Key_Recode.htm for a scan of the owner manual page on this.