It depends on why the belt came off. Inspect it carefully for cracks and for places it is not smooth at narrowest part of the V. If it passes you can try putting it back on. Make sure you inspect all pulleys and tensioners that are driven by the belt to see if they turn freely and don't wobble. Since a belt is not expensive and from my experience it often soon after fails, you should replace it. You will need to be on the alert for other problems since it sounds like the coolant was completed boiled out twice. I am surprised you didn't smell coolant, see steam or have an overheating light on the dash.

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