The brief
The 520i was throwing a low-coolant warning that kept coming back even though the reservoir was full and topped to the line. He brought it in, which is the right call, you can't just ignore a coolant warning, but a warning that won't clear on a full system points at the sensor rather than the coolant. The expansion tank, the plastic reservoir that holds the spare coolant, has a level sensor built into it that tells the car when the coolant's low. Like all the plastic in the cooling system it heat-cycles under pressure for years, and the sensor inside it can fail or the float can stick, so it reports low when the system is actually full, triggering the alert over and over. On these the sensor isn't separately serviceable, it's part of the tank, so a failed sensor means a new tank, which is the sensible fix anyway given the age of the plastic.
The diagnosis
A check confirmed it, the cooling system was full and holding pressure with no leak, but the expansion tank's level sensor was reporting low regardless, which is exactly the false warning. The radiator, the hoses, the pump and the rest of the system were all fine, it was purely the sensor in the tank. That's a tank replacement, the sensor's integral to it, so the call was a complete expansion tank with a fresh cap.
The work
The cooling system was drained enough to get at the tank, the old expansion tank with its failed sensor removed, and a new genuine BMW-spec tank fitted with a fresh cap. The system was refilled with the correct BMW coolant, bled the proper way so no air pockets were left, pressure tested to confirm it held, and the stored coolant-level fault cleared. A road test confirmed the warning stayed off and the gauge sat steady.
The outcome
No more false coolant warning, the level reading correctly, the gauge steady, and the system holding pressure. The 520i went home with the nuisance warning gone and a fresh tank in place of brittle old plastic. A failed level sensor in an ageing tank is a sensor problem and a future-leak problem in one, so changing the tank sorted both at once.