Why won't my iPhone 5 connect to iTunes?

Everytime I plug it in my computer makes the "do-do" sound so my computer knows my phones plugged in.
iTunes doesn't acknowledge it at all. I've updated to the latest iTunes and my phone software is up to date too. My phones only 1 week old and I haven't connected it to iTunes yet.
I've also tried 2 different brand new apple iPhone 5 cables but that's not making any difference either?

Unplug it and plug it back in rapidity

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