iPhone 5 does not work while charging My iPhone 5 does not respond to swipes and gestures on the touch screen, while charging.
The buttons work fine.

What is this issue, I have on 2 iPhone 5 devices - so not only one.

Rebooting does not work and hardware reset neither.

Update:


I do not have this issue via the computer (but this is a different cable as well). 
I did check this in my car, which is a Pioneer radio with USB in the front. The iPhone works without trouble in there.
At my home, the iPhone does not respond as described above. It's 100% an original charger and cable, but it might be broken as stated by KrisReynolds. Also, this house is built in 1970 by my Grandfather and the wiring sometimes is pretty poor. This might be the cause too.


Update 2: The bounty and the accepted answer are both great - couldn't decide so I split the accept and the bounty between them.
The problem is the electrostatic current/charge/grounding while using Charger.

First make sure you do use the original Charger.

If your iPhone is in a leather case, remove it.

If you have a protective case, or if you are using a plastic sheet or film on the display, try removing them and testing the device without it.

Update: 

I missed the point of you having 2 other devices doing the same.

In that case it could be the electric wiring in your place. Try plugging in in a another place (coffee shop). You might have what it is called High Frequency Harmonics (dirty electricity) in you home caused by number of different sources.