I replaced the battery on my old 5s and now it will not charge.

The first thing to check would probably be the battery itself. Where did you buy it, and what brand is it? Do a google search and see if others have had problems with that brand. Unfortunately, some off-brands are just junk and not worth a purchase. Or you could have just gotten a bad battery. Try to contact your seller and see if you can arrange a replacement. If a different battery does the same thing it might be a damaged port, but I believe that it would have been doing this same thing before your repair if that was the case.

I hope you can get a new battery and a quick swap is all you need.

As others have said. This could definitely be a bad battery. If you still have it, see if the old battery exhibits the same behavior.

If not, then bad battery. If it does, this may be pry damage on the logic board. On the iPhone 5S and SE first generation there are some tiny little components next to the battery connector which are responsible for the transmission of battery data that commonly get knocked off during replacements. So power management components wouldn’t have anyway of knowing how charged the battery is. So even if it IS charging, the phone would have no idea.