iPhone 5s not charging

Hi charger, it could be your battery. It could also be the charger, cables, etc.

But, here are some basic troubleshooting steps to try first and prior to checking in with Apple support:

https://support.apple.com/en-us/HT201569

Sure, rebooting an iPhone can often help. Are you using the supplied Apple 5 watt white charging brick. Have you tried plugging in to your computer USB port to see if it charges that way? And yes, you're battery is likely in need of replacement.

It could be the battery. It could be a faulty cable. It could be dirt in the lightning port. How long has it been since you were able to charge the phone? If you have another Apple cable, try using that.

Yes, a force restart could help.

Hold both buttons down for approx 10 seconds until you see the Apple logo

And is has someone elses name and number in it? Take it back to the Verizon Center.

Sorry, you bought a phone from Verizon and it wasn't ready for the next user. Take it back. Get one you don't have to find a workaround for.

Agree with rb. Sounds like a refurbished phone in which identifying information was left on it & it wasn't cleaned up properly before reselling. Definitely take it back asap, or you'll find yourself in a more serious situation like Activation Lock

Where did you get the phone?