honestly, I do not own an E53 yet, (but I'm hear to learn about them to buy one).
BUT if your headlight system is anything like myE46 headlight system, there is usually a black rubber dust cap, or plastic covering over the back of the rear of the HID system (like on an E46 M3).
once you remove the dust cap, you should see a fat red wire running to a black plastic screw fastener. you have to turn this fastener slightly. Be warned, it is often very tight in this area and difficult to turn this piece.
once you remove this, you can freely pupp the HID tube (bulb) out and replace with a new one.
remember when screwing the black plastic fastener back on, it needs to snap into place to make a sure connection.
make sure you put the rubber dust cap on again to avoid build up inside your lighting system.