Famous hacker iH8sn0w updated his Twitter account with a tweet about the release of untethered jailbreak on devices running iOS 6.1.3 and iPhone 5 iOS 6.1.4. The latest info he posted on his blog where you can find info not only about jailbreak but more news regarding iOS 7 custom IPSW, fetching iOS 7 SHSH blobs by iFaith and iTunes 1.1. Error 11. You can also save iOS 7 SHSH using TinyUmbrella,  just in case. But because of new iTunes 1.1 it is impossible to restore device using custom IPSW. So don't wait for PwnageTool, Sn0wbreeze or redsn0w or seas0npass. And it is really bad news. Let's hope for better days and time for hackers to update these tool for the new iOS

As to iOS 6.1.3 - 6.1.4 jailbreaking iHsn0w wrote this:

Everything for a 6.1.3/6.1.4 A5+ jailbreak is there. We're focusing on fixing bugs that occur internally. These range from Applications automatically deleting themselves from the uicache to iMessage/Facetime activations not working (even on legit sims). As far as a time frame goes for fixing these bugs, we have no idea.

There is no time or date but news are good. So if you are lucky to stay on iOS 6.1.3 or use your iPhone 5 on iOS 6.1.4 you will be happy to get untethered jailbreak soon. The developer also mentions about iOS 7 jailbreak and he told that this question was not to him. This development is on evad3rs team and many hope that they will finish it soon. Meanwhile there is no fresh news from members of evad3rs group.