I assume the X had all four wheels off the ground to do the boot. If so, it could also be a rear sensor. Good idea to check all sensors first!

The X is very sensitive to voltage loss or fluctuation. One of the most frequent symtoms is what you are experiencing. Since you don't have the tools or the place to work on your X, I suggest you return to Autozone and ask if they can safely test your charging system. The sensors could all be in the correct position and working fine with a voltage loss or fluctuation. This assumes the other lights that came on when you got home were the same or just as confusing as before you purchased the battery.

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