IPhone 5s Shut off and won't turn back on

I have had my IPhone 5s for about a year and this issue just started the other day. At first my phone did a auto reboot then operated normal later that day it did another auto reboot then went to a blue screen. After about an hour or so it rebooted then returned to normal operation. Yester it did the same thing so I did a factory reset and restored from my last back up. The phone operated normally all day until last night when it did another auto reboot then went to a blue screen then did another auto reboot and went to normal operation. Today it was operating normally and I went to use my phone and it is just a black screen. The phone was charged to 100% when this happened. I can not get my phone to turn on. I tried the hard reset. I tried plugging it in. Not sure what to do. Half tempted to just upgrade to the 6 but I'm afraid that when I do the restore I will I have the same issue with the new phone