You will need an Adapter for the 5S to go from BRP 30 pin Spyder cable to Apple Lightening connector used on your 5S.
Make sure you get a real Apple adapter as most the after market adapter charge only. They do not do "data" connection which is what the Spyder needs.
With your Spyder you should have gotten a cable for the port that is in the trunk on the right side.
Here are what the BRP iPod cables looked like. The one with the box in the cable is 2010-2012 and was later change mid 2012 and up for a cable with no box on it.
http://www.spyderlovers.com/forums/a...5&d=1448381732
Bob