iPhone 5s Fm transmitter/charger

I had an iPhone 4 and with it I had a Belkin fm transmitter/charger for my car. Since getting the new iPhone 5s, I realize I can't connect that transmitter to my new phone.

I'm looking for one of two things:

1.) a way to continue using my existing transmitter/charger, as in is there an adapter I can attach?

2.) Or, a recommendation on a new transmitter/charger that isn't a fortune. Best Buy only had one and it was $80 (Can$) and it looked horrible.

Lastly, I was told by a woman at an itech kiosk in the mall that iPhone 5 cables don't work with 5s. Is this true? I want to believe her because she actually did plug one it to try it and it didn't work, but for all I know it could have been that one knock off cable.

Thanks in advance!