Computer won't recognize iPhone?

I just got a new iPhone 5 and wanted to sync it with my iTunes account to replace previous music and pictures, but neither my windows computer or iTunes will recognize it. I've tried a different cable, but it still didn't work. When I plug in my old iPhone, everything works fine & it is recognizable. It works on a different laptop, but not mine. Any help?

Do you have the most current version of iTunes?

I found this solution to work. Try this first:
a) Get Windows to restart the drivers:
- disconnect your USB device and close ITunes
- connect your USB device
- if ITunes loads, close it.

b) File explorer:
Open File explorer and browse to
C:\Program Files\Common Files\Apple\Mobile Device Support\Drivers
In that folder there should be a set of files named "usbaapl64…"
right click on the one ending in "INF"
Select Install. It's very quick.
remove the USB device

c) Restart the computer.
When you login again, load ITunes before you attach your USB device.

d) If still not works, try re-install iTunes. Go into the Unstall Programs (in Control Panel) and uninstall everything that says Apple, and uninstall Bonjour. With the fresh install of iTunes, everything came back and is should work. Hope it helps.

f) If you just want to add some photos, songs and movies from computer to your devices, you can use an iTunes alternative to do the job