Yes. But make sure to restore to iOS 6.1.4 then update to iOS 7, just in case.
I didn't that at all. So when it was at the "bar" screen where you see the logo and a tiny progress bar, it froze there forever while iTunes didn't 'even show the device is connected when it was.
So I just unplugged the iphone 5 and it reset itself to the "restore from iTunes" screen (which is also new now).
Then I proceeded to update the iphone 5 with ios 7 and it worked.