I have owned and shot both extensvely. I see no advantage when comparing them. I still own a KS-5 (given and fitted to my wife). I personally shoot a K80 Trap special combo....now there is a definite difference.
In my opinion, either of the "K" 5's are solid guns and will do a great job for a shooter. They are well built and will last a long time. My only complaint is that then locking/unlocking lever also cocks the gun when opening...I found this to require extra effort. Other than that....both are great guns.
KX-5 has a different forearm iron. The KX-5 forearm wood butts up to the forearm iron near the hinge pin, while the KS-5 forearm wood extends down to the hinge. KX uses a push button release on forearm. KS uses a lever release.