The brief
The 520i had picked up heightened vibrations, an unsettling knock when shifting gears, an unusual amount of drivetrain movement, and a change in how it handled. Those point at the propeller shaft mounting. On a rear-drive BMW, the propeller shaft runs the length of the car to the rear axle, and it's supported in the middle by a centre bearing held in a rubber mounting bolted to the body. That mounting takes the shaft's vibration and locates it. When the rubber perishes and the bearing wears, the shaft can move around, which is the vibration, the knock when the drivetrain loads up on a gear change, and the changed feel. A worn shaft mounting only gets worse, and it can put extra load on the joints and the bearing, so it needs changing.
The diagnosis
On the lift the propeller shaft mounting was checked, and the rubber was perished and the centre bearing had play, letting the shaft move more than it should. The shaft itself and its universal joints checked out, so it was the mounting at fault. That's a mounting replacement, the centre support bearing and its rubber mount, rather than leaving a worn one to load up the rest of the shaft.
The work
The propeller shaft section was supported and dropped enough to reach the centre mounting, the old worn bearing and rubber mount removed, and a new genuine BMW-spec centre support bearing and mounting fitted, the shaft reinstalled and the bolts torqued to spec with the shaft set straight. A road test confirmed the vibration and the knock on gear changes were gone and the drivetrain felt tight again.
The outcome
No heightened vibration, no knock on gear changes, no excessive drivetrain movement, and the handling back to normal. The 520i went home with the propeller shaft properly supported again. A worn shaft mounting only gets worse and can take the joints and the bearing with it, so changing it kept the drivetrain right and headed off the bigger repair.