I really think that you have a short. I have never seen a fence with all five strands hot. Around here we make one or two hot and the others are grounded. That way if you touch two wires you have touched a hot one and a ground. If you really want all five hot. Try disconnecting one at a time and see if it does not pick up shock when one of them is out of the circuit. If it really is the ground and it can be. Try making every other wire hot and ground the others. That is the way the ranchers do it who have 50 miles of fence
Everyone here that I've talked to runs all their strands hot. I have a parmak book and a gallager book and both show that both methods can be used. Here is a parmak link showing both strands hot with earth ground.
PARMAK USA - Recommended Outdoor Installation
hmmmm, I do however have a utillity ground closer than 50' to my ground rods. Actually the utillity ground is on one side of shop about in the middle and charger grounds are on adjacent side . I'll disconnect ground wire from utillity ground just for a temporary fence test and see if this is the problem. If this is it I'll move the utillity ground farther away.
Ken