Some people have run into a dreaded blue screen of death bug which seems to be related to specific apps. If you are using Pages, Keynote, or Numbers and you are in a document editing, then pressing the Home button can cause the iPhone 5S to crash to a blue screen, which is generally followed by a reboot. Some people are reporting this issue with other apps as well, and in severe cases it is causing a reboot loop. There’s a theory that the iPhone 5S is afflicted because it has a 64-bit processor trying to run 32-bit software (it’s the first 64-bit phone). Developers are already updating apps to work with the new processor more fluidly and Apple will likely release an update to fix it at some point, but in the meantime there’s no solution, only workarounds that have worked for some people.
Always make sure you back out of documents before tapping that Home button.
Disable iCloud sync for the iWork apps by going to Settings > iCloud > Documents & Data, and sliding Pages, Keynote, and Numbers to off.
Try to use apps that have been updated to take advantage of iOS 7. Apple has not updated Pages, Keynote, or Numbers. You can tell
If the problems are constant, or frequent to the point of impeding your experience, please contact Apple customer service