Is the iPhone 5s physically similar enough to the iPhone 5 to use a close fitting case? I wonder if there is any reason why a close fitting iPhone 5 case wouldn't also fit the iPhone 5s? It would be helpful to know whether the cutout for the camera or the various buttons (mute switch, sleep, volume) and lightning connector are close enough for hard cases to fit between the models (or vice versa).
Per Ars Technica:


  "Every measurement, right down to the 3.95 ounce weight and 0.30-inch thickness, is identical to the iPhone 5."


Visually from looking at photos the ports, buttons, etc. are all identically placed. Also, one of the image captions in that article:


  "The leather cases for the iPhone 5S will also fit the iPhone 5. This should also hopefully mean that third-party cases for the iPhone 5 will continue to fit the 5S."


The only possible issue would be the iPhone 5 LED flash vs the 5s' dual-LED flash. But as long as the cut-out on the third-party case looks like Apple's does (i.e. it goes around the camera and the LED in one cut-out), there shouldn't be any reason they don't fit.