It is normal for the engine to initially idle higher. Assuming it is higher than normal it could be an issue with the idle control control valve but I wouldn't be buying parts yet. If you have a way to check codes there may be an error code that helps finds the problem. As you have described the problem, it doesn't sound like a low fuel pressure issue to me. Are there any other symptoms such as loss of power, missing or fluctuating idle?

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