IPhone 5s won't sync/connect to Itunes?

I recently got a iPhone 5s and I tried to plug it in to my computer to sync my music that was on iTunes onto the iPhone. But my computer wouldn't recognize my phone on iTunes. It worked when I had my iPhone 4 but it stopped working about a week before I got my new phone. I've tried multiple methods on the Apple help page to fix it but I always keep running into an error. Anyone know how to fix it?

Did you try plugging the iphone into your computer while pressing the home button? Also, after you plug in the idevice to your computer, and after a few seconds the idevice should ask you if you trust this computer, enter yes. Finally also try updating to the latest iTunes… This are the steps I've taken when I had similar problems, good luck!