Why is my iPhone 5 turning itself off after I turn it back on?

My iPhone 5 is messing up on me. Although there is one problem I have with it. I was getting rid of some iCloud storage then I turned my phone off. When I turned it back on again, it just turned off itself the minute it turned back on! I plugged in the charger and tried again after a minute. It still didn’t work! I tried rebooting it but it was no use. Any help please? I would really like it.