You came to the right place for assistance yotie! Let's get your iPhone 5s charging again. May I ask are you using the original manufacturer's charger? Also, are you charging it in the wall? Can I assume that there isn't any liquid/physical damage on the charger or the iPhone? As you share the details then we can assist.
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this phone is in top condition. protective case with crystal screen protector also. it would pass for brand new in the box. never been wet and the charging cable was purchased from my local Verizon store here. all origanl equipment. I don't think its the wall charger itself, more the port on the phone. I can wiggle the cord and after sometime get it to stay connected for a charge. but just to say, plug it in and lay it down? not a chance. the phone is maybe 6 months old at best. never dropped banged around nothing.
This happens to laptops a lot because the cord gets tripped over or pulled on and bumped etc. You can buy a replacement port for dirty cheap, but because your phone is still under warranty you'd want the Apple store to replace it for you. Screen replacement is around $100 and that includes the part, I'd like to think it'd be much cheaper to replace a $5 part.