BMW E60 automatic gearbox jerks when pulling away cold

The gearbox torque converter lock-up only engages once the gearbox oil has warmed up to about +35 degrees. Until then the gearbox may jerk or judder. The symptom usually disappears when warm. If the jerking continues when warm, it is a fault.

A gearbox software update at a BMW dealer or specialist helps most often. It removed the lurch when pulling away and the symptom did not return. An oil change and resetting the adaptations (the values the gearbox has learned) can ease the symptom, but resetting alone is not always enough.

Yes. Jerking can also be caused by the engine: injector faults and a glow plug fault made a cold car jerk at idle. If the jerk comes when you lift off the throttle, also check the propshaft flex joint and centre support bearing, and the driveshaft play.