Could be a number of things really. When do you hear the noise? When you accelerate from a stop, when you turn or brake? Do you hear it from the front, center or rear of the car? Any vibration to go along with the noise? What you need to do is get a friend and raise the hood and put the trans into drive and hold the brake with your left foot. Gently apply the throttle while someone stands to the side of the car near the fender and have them watch for the engine to move an abnormal amount. Do the same in reverse. Go back and forth and you'll be able to see if there's a bad engine mount. My guess honestly would be a bad differential mount, but I wouldn't rule out an engine mount.
Welcome to Bimmerfest! I've moved your question to our E39 5 Series forum. Without more info on when the noise is happening it is hard to diagnose. Have you replaced any of the bushings on your car? At that age almost everything is probably on it's way out.
Definitely sounds like the differential bushings. We had a similiar issue. Put the car in park, look at the diff when someone is rocking the car back and forth, we had a good 2 inches of up and down play.
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