[HELP] Unrooted Nexus 5 randomly shut off, now frozen on Google logo at startup

I didn't drop it or get it wet or anything, it was just sitting on my desk and it randomly shut off. I've tried shutting it off and on again but it just comes back to the google screen where it sits frozen for about 30ish+ minutes before it shuts off, I can't turn it off otherwise, if I try turning it off it just turns itself back on so I can't shut it off. Is there anything I can do to save my data (or even better, fix my phone) or am I screwed? I also don't have USB Debugging turned on so I can't get stuff back that way either. My phone is not rooted and running stock android 5.1.? (Don't remember my exact version but I think I've missed the last 2 minor updates)