Adapter from iPhone 4/4S to iPhone 5/5S?

Up until last week I had the iPhone 4S. For my birthday, my boyfriend surprised me with an iPhone 5S. Last Christmas he bought me a docking station (Sony ICF-DS15iP) and I absolutely love it, it's the best one that I could imagine. Obviously my old iPhone has different connectivity slots than my 5S. All of the adapters that I have looked at only transmit charge and won't transmit sound through them.

Can anybody point me in the right direction please?

The genuine Apple adaptor runs most accessories including analog audio ones.
http://store.apple.com/...in-adapter
They work better than the generic ones. About the only thing I know of they can't handle is remote ipod controls.