In the screenshot seen below, Cydia is shown running on the phone. At the very bottom of the screenshot you can see the iPhone 5 device and iOS 6.1.4 firmware specified.
About a week ago, winocm announced that he had a binary that would perform an untether of the iOS 6.1.3 jailbreak. At that time he had only tested the jailbreak on an iPhone 4.
It appears as though winocm's work on the jailbreak has progressed to the iPhone 5 and iOS 6.1.4. At this time there is no ETA for release; however, you can follow iClarified on Twitter, Facebook, Google+, or RSS to be informed of any new developments or release information.
Update: It looks like winocm was also able to get the jailbreak working on the CDMA version of the iPhone 5 as well.