Iphone 5 - won't turn on properly and screen shaking

Hi there,

My iPhone 5 ran out of battery and when I charged it up and it turned on, the screen started shaking. I decided to restart it but had problems turning it back on the start up screen comes on then cuts out. When eventually it did turn back on the screen was still shaking so I decided to try to update the software it to see if that helped. However after the software update it still happened and now my phone won't turn on it keeps cutting out on the start up thing.

Anyone know whats wrong or what I need to do?

Thank You