Iphone 5s only vibrates but won't connect to computer?

So I bought a brand new Iphone 5s and when I went to sync it my laptop it just vibrated and switched back and forth from charging to not charging. I don't think it's the phone and may just be the USB ports but I'm not entirely sure. Any tips?

What length cable are you using? Maybe the USB port isn't supplying enough power. Are you using a laptop or Desktop? If it's a laptop, try plugging the laptop in to the mains. If you are using a cable that is longer than 1m that'll be your issue. I have a 2m cable for my iPhone and I can't plug my phone into my MacBook with it as it has this exact issue. A USB port doesn't supply a lot of power.