Yikes. That's not good. I haven't got the opinion from the forums that the 5s has more hardware issues than expected. However, iOS 7 is a steaming pile and you can't separate the two. As the other poster mentioned, restoring from a backup can be problematic. The other biggest thing is a misbehaving app. I'm trying to be helpful when I say "most" people don't have that issue (maybe lots, but not most) so take a look at what apps are on your phone and look at folks talking about their blue screens and maybe you'll make a correlation. Whatever it is I hope you get it figured out.
As a test, backup your phone and then restore as new and don't do anything else. Does it still happen? Start installing your apps with an evaluation between installs. If you can't reproduce it then it's something with your backup. If you restored from a local backup try from the cloud if you have one. Or the other way around. 🙂 Unfortunately, simple detective work at this point.