The latest operating system to come from Apple is iSO 7.1.1 and many people went ahead and rushed into updating their handset. They then realised that they couldn’t jailbreak their iPhone, but there wasn’t any way of going back. Things have changed now and you can revert from iOS 7.1.1 to iOS 7.0.4.
The device used to test this was the Verizon version of the 64GB iPhone 5S, along with OSX 10.9.2 and iTunes 11.2.2(3), it should work with any iPhone though. This was also done through iTunes.
So to start you will have to plug in your iPhone 5S and wait until iTunes shows that the handset does have the latest OS. There should also be a prompt asking you about restoring a back-up and it you click this it will show you the older iOS.
Click this and the handset will go back to the older iOS, but you could have some data missing. If your backup is corrupted you can use iPhone Backup Extractor.