At 88,000 miles, and no blue smoke out the back, I would want to know how long the O2 sensors have been in place. If you don't know or they are original I would check or replace pre cat sensors. That could be the cause of cold rough idle. O2 sensors don't cause a fault but it does usually show as a lean condition. When you say it is not showing any error messages, is that from using BMW diagnostic equipment?

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X5 4.6 2002 Black Sap, Black interior. 2013 X5M Melbourne Red, Bamboo interior
Dallas