If I do a factory reset on my iPhone 5, will my phone go back to iOS 6?

I hate the new update, my phone works terribly now

Only if you had iOS 6 installed to begin with, apple has made it impossible NOW to revert back from iOS 7 to iOS 6. We could earlier on, but we missed the boat.

Yes, of course you can't. Because Apple has been un-sign the old iOS 6 version.

No i tried myself. It doesn't help at all.
i had installed iOS 7.0.4
i did the reset and other thing it doesn't help.

Factory reset just takes your phone back to how it is if you buy it new but will load the latest os you had on it when you did the factory reset so if you have ios 7 that is what you will get back. Apple did that to stop anyone rolling it back.