At least on the E46 and I think the E39 with the 6 cylinders the engine to body ground happens to be on the passenger side near the motor mount. Often you have to remove the lower engine cover to see them.
Not sure if the E53 is set up like the E46/E39, but usually you will find a frame rail connection near or just behind the strut tower. Look around the motor mount area to see if you can find the ground.
Here is a picture of the strap on an E39 which is a 2nd cousin of the E53 IMHO -
Bimmerfest - BMW Forums - View Single Post - 2003 Ground Wire on shock tower?