iphone 5s is blinking on and off

Hello,

Please describe your problem in more detail. What is blinking? What are you doing at the time?

If your iPhone, iPad, or iPod touch won‘t turn on or is frozen

Good luck.

Hmm it would be good idea touch base with Apple support regarding this one.

If you've got any important data you need to keep make sure it's backed-up on iCloud or iTunes.