Some guy on another thread said all 4 replacements had the random reboots! I'm getting mine replaced next week so I really hope I'm not as unlucky as him.
It will be fixed.
Seriously - what do you expect from a *hardware* replacement when it boils down to being (most likely) a *software* (iOS 7) issue?
Or did the colour already come off your 5S?
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We all live in a happy "no bad karma" Apple world! Sing along!