$COUP_COMP of A4, A5 and A6 finetuning?

While I'm not personally familiar with $COUP_COMP, the {N,D} structure looks very much like $RAT_MOT_AX and other "gearing ratio" variables. The N is the Numerator and the D is the Denominator of a fraction. The fraction represents some sort of motion ratio between one axis and another. Exactly how they interact I don't know, however.
If I had to hazard a guess, I'd say that the first is the relationship between A4 and A5, the second is A4/A6, and the third is A5/A6. I'm not sure tampering with these variables is a good idea, but if you want to try it, I would try making very small changes to the N value of 4/5 until you null out the movement of A5. Whether the N value needs to become larger or smaller you will have to determine empirically. If changing the N value alone turns out to be to "coarse," you might try multiplying both N and D by 10, then changing N incrementally, in order to increase resolution.
If that works, I assume you could continue down through 4/6 and 5/6. However, I have to wonder how changes to 4/5 might interact with 5/6, and vice versa. You could end up in a wild goose chase.

Is that not normal that the A4 and A6 are driven aswell when moving the A5 with KUKA Robot?

Depends on wrist design. In general, A4-A6 share a gear train, so to move one axis while keeping the others stationary may require turning all three motors -- one to move the commanded axis, the others to counteract the gear train side effects cause by turning the first motor. But, looking at the actual wrist joints, ideally one should see no motion on A5 or A6 when moving A4 in isolation -- the motors may turn, but the physical axes and the values of $AXIS_ACT should not. I assume that $COUP_COMP defines how much "counter-driving" each axis needs to offset the side effects of turning one of the others.