Not exactly an engine flush but I used to do it on all my E39's...
Drain the oil, put the plug back, pour in the engine 1 gallon of diesel , start the engine briefly for 3 seconds then shut off, let it sit for about 15 seconds then start again for 3 seconds and turn off.
Drain the diesel , follow with the filter and oil change.

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2006 X5 4.8is LeMans Blue / creambeige interior
Prod.date: 2006-06-21