Is it possible to downgrade from iphone 5 ios 7.1.1 to ios 6.1.4?

My iphone 5 came with ios 6.0 and i backed up my SHSH before updating to ios 7 and backed up to itunes, so is it possible to go back because i miss ios 6

Nope

Unfortunately there's no way of downgrading on your particular iPhone 5. Even though you backed up the signature hash blobs, nobody has been working on a boot ROM exploit ever since the iPhone 4s came out.

Your best bet is to actually trade the iPhone 5 with another iPhone 5 that runs iOS 6.1.4. Just so you know, you won't be able to use face time since Apple has decided that iOS 6 should be left cold.

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