There are soooo many things in an e53 that can kill the battery. Mine was the Bluetooth module (tcu). Unplugging it is a simple test to see if that's the issue on it but again there are tons of possibilities.

But if you have the Bluetooth unit its a good a place as any to start. Search the forum for what to unplug there are post with pictures of it.

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Aftermarket E53 Radio Install