There is a visible dot on the iPhone 5s between the rear camera and the LED flash. What is it for? I imagine it is a sensor of some kind.
I'm concerned because my new iPhone 5s case covers it.
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It's a microphone, useful for video recording using the rear camera and for digitally eliminating background noise when you're on a phone or FaceTime call. Source - Apple support.
Apple doesn't have an explicitly stated opinion on whether or not the rear microphone absolutely can't be covered, but in that support article,
Remove screen protectors, films, or cases that cover the microphone, iSight mic, or iPhone receiver.
is the third recommended step for people experiencing microphone issues.
That is a microphone. I wouldn't worry about a case covering it too much, as your iPhone 5s has multiple microphones on it. Obviously it would be better if the case didn't cover it, though.