CJ5 pulls to left and right on acceleration/deceleration

sounds like a steerring pump or rack and pinion issue....

Oh wow since when did a cj5 have rack and pinion? Its a couple things its old has led spirings that will dog walk and your rod ends are worn out jack it up and grap the wheels to see if their lose.

ah still new to jeep sterring system i havent tooled much with my cj....

How long have you owned the old Jeep? Sounds like someone could have snuck in one of the less expensive (but still very good) rear lockers. Sometimes they'll do that on acceleration and deceleration. It's most noticeable right after making a turn. Having said that, it could also be as the other fellow says, CJ's were notorious for unexpected movements while underway, due to the arrangement of the front spring hanger. Most automobiles are set up with the hanger in the rear and the eye in the front. CJ's are one of the few that are not so, this, as the bushings wear, causes unpredictability while at road speeds. Take a look at the hanger bushings at the front end of your front springs and make sure they're still pretty tight. Any slop, not good.

Welcome to the CJ5 world, We can'not be beat off road. Get off the pavement, it's like trying to drive a snake on the street. You did not say if it has been lifted, that can cause several problems in the steering. CJ5's do not go fast. If it has not been lifted 32" tires are about as large as you can go, Check your steering linkage and bushings, very important and enjoy the best off road vehicle ever built. The steering is very exposed in the front consider getting a skid plate to protect the steering box.