The brief
The 520i had a vibration the owner felt through the cabin floor, a knock every time it changed gear, and a distinct clunk whenever the drivetrain took up the load under throttle.
Those three together point at the propshaft. On a rear-drive 5-series the engine's torque runs back to the rear axle through a long driveshaft, and where its sections meet there is a rubber coupling, the flex disc, that lets them move a fraction without binding. When that coupling cracks and goes soft, the slack shows up as a knock on take-up, a clunk under load, and a buzz through the floor at speed.
The diagnosis
On the lift the flex disc told the story straight away. The rubber had cracked through around the bolt holes and lost its shape, so the propshaft sections were no longer held tightly to each other. The shaft itself ran true, it just was not being coupled properly any more.
There is no patching a perished rubber coupling, and letting it carry on would eventually let the propshaft thrash about under the car. The fix is a new flex disc, fitted in the correct orientation with fresh bolts.
The work
The propshaft sections were unbolted at the coupling, the old flex disc taken out, and a new BMW-spec disc fitted in its place, lined up the right way round, with the carrier and coupling bolts torqued to the manual figures.
Then the propshaft was reconnected and the car run up through the rev range to confirm the drivetrain spun smoothly, with no knock on take-up and no clunk under load.
The outcome
No more vibration through the floor. No knock on gear changes. No clunk when the drivetrain loads up.
The 520i went home with the drive running smoothly from the engine to the rear wheels again. For the owner that is the everyday difference, a car that pulls away cleanly instead of knocking, and feels tight rather than loose under power. And catching the perished coupling now meant a straightforward swap rather than a propshaft that eventually flails itself and the tunnel above it.