When i go to put my car in reverse to back out of the driveway, as soon as i let off of the brake, i can here a loud pop sound that seems to come from the rear of the car.

Im thinking its originating from the rear axle, but im not sure

Has anybody else had this problem, or know what it might be?

-Thanks

my first thought would be the torque arm mount . the rubber bushing/mount could well be 25 yrs. old and sloppy . next would be trace brace/panhard bar loose or bolts fell out of mount to body ( happened to me ) . good idea to replace any/all suspension bushings , 25 yrs. are not kind to the rubber bushings . they are cheap , and can be replaced one at a time . good luck .

Check your u-joints. Cheap and easy fix.