The start up whistle may be the auxiliary engine blower fan. Located on the fender right side. It runs a few seconds at start up to add air into the exhaust. Mine failed a while back. Took three units to keep the service light off. A Hella replacement air pump works great. Two other brands didn't work. If the noise is inside, it's probably the blower motor fan. Mine does it too. Mostly while driving though and not often.

Fuel and bad battery are my primary guesses. Check the battery voltage. If the battery is over three years old, I would definitely keep it on a trickle charger.

Wow, low mileage survivor. Post a small pic or two of it.

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'06 X5 3.0i - bought @143,123 miles (12/26/20)