While not exactly common, a good many folk have had an electrical drain issue on the E53. And it's not necessarily related to the alternator.

What was the diagnosis of the bad alternator based on - just the battery going flat or was the alternator output tested?

Many modules in the E53 can cause an electrical drain - often by keeping the car "awake" and not letting the car drop into "sleep" mode (which should happen 16 minutes after you shut the car down - assuming no further electrically activity occurs).

While it's not a definitive indication of a problem, the orange LED near the gear selector can indicate the sleep state of the car. Does your orange LED near the gear lever go out after a while or does it stay on always?

If it stays on, you *may" have an electrical drain issue and will need to perform electrical drain testing to determine if this is the case and if it is, what module is causing it. Radio, Nav, ULF etc. have all been known to cause battery drain issues.

You can also monitor the battery voltage while the car is running, to check if the alternator output is good. This is done by unlocking the diagnostic menu on the cluster (called the "board computer", BMW Computer or simply BC). There's plenty of instructions on here about how to do this.

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Wayne
2005 BMW X5 3.0d (b 02/05)
2001 BMW F650GS Dakar (b 06/01)