Turn the charger the other way
I, too, am having the same problem charging iPhone 5. For those of you that live far away from an Apple Store, I seem to have found a temporary solution. All you need is the charger and a small enough elastic band of any kind (rubber band, hair scrunch thingy, etc.) In my case, pulling the cable to the left side of the phone drew a full charge. The band keeps the cable in place wherever your cable 'connects.'
It works for now.
Apple
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