My iphone5 started blinking the Apple Icon, on and off. The phone will not let me turn it off. Any Suggestions? and why is this happening?

Try a device reset:

Device Reset (won't affect settings/data/music/apps/etc)

1. Press and hold (& continue to hold) BOTH the Sleep/Wake button & the Home button.

2. Continue to hold BOTH (ignoring any other messages that may show) until you see the Apple logo on the screen.

3. Release BOTH buttons when you see the Apple logo and allow the device to boot normally.

Try doing a reboot by holding both the power and home buttons, at the same time, until the apple logo appears, about 10-30 seconds, then release both buttons, let it finish the restart procedure, and see it the iPhone will allow you to do a normal power down.