Put a voltmeter across the battery terminals and check, with the engine running, for around 13.85 volts. If it drops below 13V you most likely need an alternator.
If you are not comfortable with doing this any Autozone, Advanced Auto, O'Reillys or the like will do a free battery/charging system test.

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