If your iPhone just shows a battery icon with a red strip on the left and won't take a charge, you may need to warm up the battery to "jump-start" it. This video shows how. BTW, before you do this, try the simpler fix of holding the power button and home button for a really long time (over a minute) in order to reset the device. And if that doesn't work, try toggling the ring/silent button up and down twice, then holding the power and home button for at least 30 seconds. But if these simple button presses don't work to wake up the phone, then try this little trick with a hair dryer - it may save you some grief and get your iPhone back up and running.

Note: remove any protective case before warming up the phone and do keep the charging cable plugged in while you warm up the phone.

After doing this trick, we've been able to restore relatively normal operation to the iPhone 5, but the battery continued to degrade over time. Eventually we replaced the battery with a new one and got about another year of life out of it before the phone wore out.

If you're interested in replacing the battery on an iPhone yourself, you can get kits on Amazon for between $20 and $25 for most iPhones. Just be sure to get the specific battery you need for your specific iPhone model. Here are a few options: https://amzn.to/2HLulAW