My iPhone won't charge

Recently my phone hasn't been charging. It does the thing that if you move the cable it charges, and it depends on where the cable is positioned if it charges or not. So it led me to the conclusion I needed a new charger. However my phone does the same thing with the new charger, and my chargers work perfectly fine with other phones. Both chargers I need to push slightly up to make my phone charge. Any ideas on what's happening? This all started out of the blue. (I have a 5c by the way)