Chosen Solution
I have just replaced the casing on my iPhone 5s, everything else works but the lighting port. When I turn the phone off and then plug it in it will turn on but when it turns on it wont charge. I tried cleaning out the port as well as using different cables. Please help me come up with a solution.
Replace the lightning flex by @benjamen50
It sounds like a bad battery. It sounds like it would need replacement. I have the same problem with my 5s, I replaced the battery and it was working as new again. Edit: This looks like the battery you would need: iPhone 5s Battery