The manual has it right. There is a snap indent so the bulb and socket should release without too much pressure. As your turning counter clockwise apply some force toward the housing to help. I would think a better description would be "turn it counter clockwise like a thumbscrew". I do recall some frustration during my first attempt so your not alone.

PS, I just went and checked mine to make sure my advice is correct. Make sure you are turning the bulb socket which is located just below the wire connector. One may mistakenly think the wire connector is the bulb socket. The bulb socket is round, not rectangular!

PPS, once you remove the socket check the contacts where it engages the housing, they are known to corrode and burn. Good luck.

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2013 X5 3.5i M Sport
2004 M3 cabriolet SMG