Do you have the hub nut socket? The big 2 1/16" one?
It's been 20 years since I messed with a CJ5, but from what I recall, look inside the hub and see the big hub nuts, they are about 2" OD and held in place with locking tabs on the washer that is sandwiched between the inner and out hub nuts. Take a flat screwdriver and punch, wedge up where on edge fo the locking washer is flattened against the nut, carefully use punch to un-flatten it enough to get the big socket on the nut. Then remove the outer nut with the big socket. It's RH threaded like normal. Then remove the big locking washer, then remove the inner nut with the big socket. At this point the bearings and hub should be free. Then pull off the complete hub assembly with bearings. The outer bearing will fall out, so catch it. The inner bearing will be trapped by the oil seal.
Once you have the hub off, then unbolte the backing plate and spindle. The plate will come off, then the spindle. The spindle will probably need some encouragement from a dead-blow hammer. Just tap it on the sides until it's loose. Then it should come off, and then the axle shaft should pull right out complete with U-joint and inner shaft. As gunked up as it looks, this may take some work to get it out, but it should pull out, I think.
Someone will surely be around shortly to tell you how to do it right.