Phone has black screen and occasional blue screen

This iphone 5s has been working properly since my brother got it. However recently the phone randomly kept crashing and now it is going through weird stages. The phone will turn on but not boot up. From the apple logo boot up it goes into this black screen and stays there. The phone will continue to get hot and then the message to plug iphone into itunes appears. After about 5 mins the screen will flash all blue and slowly fade away. This cycle continues to happen over and over. I tried to plug it into itunes and itunes does recoginze the phone in recovery mode and tries to restore and up date but it only goes to "waiting for iphone..." and times out. The most progress I've seen is the loading bar for software installation appear on the phone for 3-4 mins before it flashed blue and went dark. The phone is running some version of IOS 8.0 not sure exactly. But yeah my brother never really updated it.