I have an E39 5-series (1998 528i) and E53 X5, basically same tricks:

1. Engine COLD.

2. Open the bleed screw near thermostat.

3. Fill the reservoir above MAX by about 1-2 inches, the key thing is PATIENCE! Sit and wait 2-3 minutes, you will see coolant coming of the bleeder screw hole near thermostat.

4. Now close the bleeder screw (gentle, no need for force).

5. Re-install the reservoir cap.

Test drive around the blocks for a good 1/2h. Let the engine cool down. Check coolant level 1h later when engine is COLD.

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1998 E39 528i 5sp MT
2006 E53 X5 3.0 6sp MT