My 5s battery died! What can I do?

Help here > If you can’t charge your iPhone, iPad, or iPod touch - Apple Support

Might also be useful to take a strong light, shine it into the Lightning connector on the bottom of the phone and make sure it is pristinely clean. I've come across more than one thread where the problem turned out to be too much pocket lint trapped in there, impeding proper electrical connection. Use compressed air from a can and maybe a toothpick to remove any contaminants.