It was a new phone, not restore as a new phone. To be honest, I don't think I had that option. I just installed a new screen on a broken iPhone 5 at work. Started using it, and when I got home where my iTunes backup is, I plugged it in and did the restore, but to tell you the truth it never asked me if I wanted to restore it as a new phone or not.
Now I know what screen you are talking about because some iPhone 6's came in and when you plug in those, it does walk through the activation and then iTunes asks to restore it along with a drop down with all the different phone backups you have, or restore it as a new phone.
The reason I have some experience with this is because at work our corporate issued phones are iPhones and the employees that have them like Executives, Management, IT, etc... require them for e-mail. We choose the Apple platform over Android because of the walled garden nature of approving apps, and with MaaS360 MDM we can enforce that they are compliant, which is very important on a device that can access company resources.
I'm thinking after going back and re-reading what I wrote, I should have done a factory reset on the iPhone 5 when I got home in order to get to the activation screen, then perhaps iTunes would have asked me if I want to restore it as a device I had backed up or new device.
I have a 6 plus on order, but don't expect that to ship for another 2 weeks or so.