I think I originally used it with a 4 with a case on it. I used mine with a 5S (with case) as well. It will work without a case, but may not hold the phone as securely. If you use the rubber band, it will be fine for most uses, though.
Also, if you click on the Remix button, it will take you to todbot's remix, which he says will fit 5 through 7 and has a Fusion 360 file in case you need to modify it. Good luck!