IPhone 5 randomly shut off with battery still remanding

IPhone 5 randomly shut off with battery still remanding. Help?

Added (1). iPhone 5 randomly shut off and won't turn back on. Help?
I was in the car and turned it off regularly and went to check the time and it wouldn't turn back on. I didn't shut it down completely. The phone was on %50 and now it won't turn back on. My power button is broken and I usually use the button in the screen so I can't reboot it. I tried plugging it in to the charger but still nothing. Apple won't talk to me since my phone is not under their coverage. I can't afford a new phone right now.

Hold the power button and the home button at the same time

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