Why are you saying that iTunes is not recognizing your Brand New 5S? After it installs the new drivers presuming for now you are on a PC and it let's you know that they have been installed you should see on the left hand side the name of your new phone which most likely is going to be the same as the old. Once you see it click on it and at the top you will have tabs telling you everything starting with a Summary from what you can select to sync and just go from there. If anything turns out to be any different, Please get back to us and we will help you to get to the problem.