Why does my laptop shut down overnight?
Your "Shutdown Cause" has three separate values:  0, 3, and 5.


"5" is a clean shutdown 
"3" is a dirty shutdown meaning the power button was held for 3 seconds or more
"0" means power loss


(contrary to what you'd think the values "should be", I know...)

There's an answer here on Ask Different that addresses the shutdown causes:  Are OS X shutdown cause and sleep cause numbers listed/explained anywhere?

A power failure on a "desktop" Mac (iMac, Mac mini, Mac Pro) is easily explained.  However, since you have a laptop (MacBook Pro), it's very concerning because if your electric current is cut, your battery will kick in and if that battery gets too low, it will save a hibernation image.  

The 0 is as if you had no battery and pulled the plug - the system just cut out.  I would take it in and have a look at it.  This is definitely not normal behavior.