Be careful where you buy the alternator. Most of the big automotive parts places use "remans" that seem to be little better than an old unit with a fresh coat of paint. I have been reading on the boards for years of people on their third or more replacement unit within a very few months of service. Go to a good online place that sells the real OEM alternator at discount (e. g. BAVAUTO) or go to a Bosch dealer. It may be more up front but sure saves a lot of headaches later. (It is your wife's vehicle, right!)
GL

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2021 X5 xDrive40i
2015 X5 xDrive35i MSport
(Traded) 2013 X5 xDrive35i