You can have a try, have some software that will help the apple system be came back.
If you can't do it youself, you can ask someone help you.
No. The only devices that can be downgraded to previous versions of iOS right now are iPhone 4, iPad 2, and previous. For those device to be downgraded, the user would have to have had to have captured the SHSH blob file using a utility like TinyUmbrella or the Cydia SHSH server thing. With that and the firmwarm IPSW file, there is a utility out there that can "stitch" the IPSW and the SHSH blob together so that the device does not need to authenticate itself with Apple's server in order to be activated. If this was not done while the previous iOS version was installed, there is no way to go back and get it. That point is mostly moot in this discussion since the OP is discussing an iPhone 5.
iH8sn0w (an iOS hacker/jailbreaker) said this on his twitter feed:
oh btw. Got another (pre-64bit iDevices) downgrade hack. Really complex. Hope to talk about it at the next @Jailbreakcon
So there is a possibility that at some point a downgrade an iPhone 5 to iOS6 will be available but we will have to wait and see if this guys work is genuine and comes to surface.
iOS 5 was never available for iPhone 5 (IIRC, it was launched along side iOS 6).
You misunderstood what I said. If you get the device from the apple store, apple.com, etc NOW its running iOS7. If you purchased it before iOS7 came out then, sure you can stay on whatever iOS version you are running because its up to you to update it.
Unless you are in a situation where your iPhone requires a restore. Then Apple will force you to update to the latest version of iOS.