This ISN'T your problem but on that year and model there was a bulletin to replace the neutral safety switch. When the car idles for 5 mins the car will go into limp mod and be stuck in 3rd gear. The switches were bad, the circuit boards went bad.

If yours has not been changed do so, they aren't expensive and just bolt on.

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2002 X5 4.4i Sport Wheels
2014 X5 35i M Appearance & suspension package
1995 Porsche 993
1972 Porsche 914-6
2020 GLE 450 Twin Turbo
2019 Alfa Stelvio 500hp Quadrifogilo
Many motorcycles