I've email Apple regards to this issue but just wanted to check if any fellow HWZ members experiencing unresponsive touch while charging your iPhone 5s. Are you using original charger or 3rd party?
Most likely due to poor shielding of the 3rd party charger/cable causing electromagnetic interference to the touch screen. Try changing to the Apple original charger/cable and see if the problem goes away. Apple original charger/cable has much better shielding that minimizes the electromagnetic interference problem.
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