The brief
The 520i kept needing coolant topped up between services, the level dropping with no obvious puddle. The owner brought it in, which is exactly right, coolant that disappears is going somewhere, and a slow leak becomes an overheat the day you don't catch it in time. When a BMW loses coolant slowly, the expansion tank is the usual suspect. The expansion tank is the plastic reservoir that holds the spare coolant and lets the system breathe as it heats and cools, and it lives under pressure and heat cycles its whole life. The plastic gets brittle with age and cracks, often at a seam or around the level sensor or the cap neck, and it weeps a little coolant that flashes off on the hot engine so you barely see it. A cracked tank only splits worse, so it needs replacing.
The diagnosis
A pressure test on the cooling system pinpointed it, the expansion tank was weeping from a hairline crack, losing pressure slowly, which is the disappearing coolant. The radiator, the hoses, the water pump and the rest of the system held fine. That's a tank replacement, with a fresh cap, rather than chasing a crack in brittle plastic that's only going to spread.
The work
The cooling system was drained enough to get at the tank, the old cracked expansion tank removed, and a new genuine BMW-spec tank fitted with a fresh cap and the level sensor transferred over properly. The system was refilled with the correct BMW coolant, bled the proper way so no air pockets were left, and pressure tested again to confirm it held with no weep. A road test confirmed the gauge sat steady and the level stayed put.
The outcome
No more coolant loss, the level holding between checks, the gauge steady, and the system holding pressure as it should. The 520i went home with the leak resolved. A cracked expansion tank only splits further, and the failure at the end is a sudden coolant dump and an overheat, so changing the tank and confirming the system kept it to a tidy, planned job.