Assuming that your 5s is out of the 1 year limited warranty at Apple, then troubleshooting the phone with the help of an independent repair shop would be your best bet.
Start with a hard reset--power and home buttons for 10 seconds. This is not likely to do much if your battery is dead, but rule it out.
If not solved, go to a quality independent repair shop where they can help you troubleshoot the following.
1--Is is just a bad battery? Cost around $25
2--Is it a bad charging port? These commonly fail since they are exposed to the elements---cost around $50
3--Are both the battery and charge port okay, but the charging logic ic chip on the board has failed due to non-Apple charger usage? Cost--around $100 as a no fix no fee solution to solve your charging problem and make the phone charge as normal. iPhone board repair is quite possible, but fairly specialized. Not all independent repair shops are capable of changing the charging logic ic chip, so you may be looking at mail in repair to troubleshoot this issue.
Your other option is an out of warranty replacement of the phone at Apple. Turn in your phone, pay $269 and get a refurbished 5s. The standard value of a good condition 5s elsewhere is less. Note: Pursuing independent repair may void your option to do an OOW replacement at Apple, although I've never seen this happen. Apple does offer a battery replacement program for $79, but they do not guarantee that this will solve your problem--if you have a charging port or charging logic ic problem, Apple can't help you.
How to identify a quality independent repair shop?
Do research. Not all independent repair shops are trustworthy, and the quality of the parts they use can vary. Look for an established shop with great reviews, a solid warranty for at least 6 months on the repair, and a guarantee to solve your problem or no fee. Ask where they source their parts. Any shop that claims to use true Apple original parts should be avoided since this is not possible. Independent repair is a fantastic option for convenience and savings, but you have to do some legwork to find a great shop in your area since there are unscrupulous ones.
Best of luck, and I'm sorry this happened to you!
Jessa