The iPhone 5 has been jailbroken untethered and there are even pictures/screenshots of it, but there will be no release until iOS 6.1 is released because if they do release it, the next day Apple will release the stable version of 6.1 so no one can update to it and get the jailbreak and like Schollian said, keeping the exploit is better than having Apple patch it, but this is taking the longest out of all iOS jailbreaks in the past because Apple have recruited a new iOS Security manager, who is smart and could patch exploits up instantly. If you would like to have a untethered or tethered jailbreak or even a semi-tethered just get your old iPhone 3GS old bootrom or new bootrom and test things out on there or the iPhone 4 or just your iPod Touch 4G as a jailbreak is ready for them and then wait for the iPhone 5 jailbreak to come out.
Many Thanks,
Software