5s dying randomly before & after battery replacement, hours to turn on

Treat any repair like surgery and do as the surgeons do: look for a noninvasive way to resolve the problem.

1. Double check the charging cables and wall adapters you are usinge are MFi Certified. This standard of certification is produced by Apple for accessory makers and certifies that your accessories will work as designed without damaging the device. If you don't have the original cases for the accessories you can use the purchase price to tell. If you bought the accessory for less than $3, chances are you don't have a certified item. It lacks the chip (which costs $3) necessary.
2. Shine a light into your charging port and look for signs of lint or dirt/dust blocking the charge. You can take a toothpick, SIM card eject tool, or tweezers to scrape out the gunk.
3. Check the SIM Card Tray area for a tripped Water Damage Indicator. This can be found by removing the tray and looking up (towards the screen) from the bottom for a little circular sticker. White = No water. Pink = Water. If there's been water damage you may be entering a "rabbit hole" of issues as is common with water damage. Best to get it professionally cleaned.
4. If you have to open the device back up start with the areas you didn't touch: The Charging Port. This is a simple fix, but can be time intensive as you have to remove a fair amount of screws and a speaker, along with adhesive.
5. If nothing else works try another battery. You never know, maybe you got a defective one.