Just saw your post where you said it doesn't sound that way at Max AC.

I think it's the secondary air pump trying to pump against a stuck closed secondary air injection valve.

See that silver mushroom sprouting from the left front of the cylinder head? That's the secondary air injection valve. There is a black hose from there going to the secondary air pump. It activates on cold starts only.

Disconnect the black hose from the valve before the next cold start and see if the sound changes.

Is your CEL lit?

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04 X5 3.0i auto
03 X5 4.6is