I agree that a fuel pressure test is good to do, however, it is my understanding your problem only happens when the conditions are very specific. That says to me a fuel pressure test may show all is well. So, I would first check to see if the OBC is storing any error codes. It's always a good thing to do first anyway but I think more important here.

May not be the case for anyone other than me but I look for anything I can troubleshoot first where there is the least risk I can cause a bigger problem and is minimal cost. If you don't have diagnostic capability the pressure test will cost less as even if you don't have a fuel pressure gauge you can get a loner from many auto parts stores with a deposit that is returned when the tester is returned.

If you choose to do the pressure test first, I would do the test with the engine cold and in the conditions you experience the issue especially if it happens every time and always in those particular conditions.

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