Jailbreak for iPhone 5 iOS 6.1.3?

I'm looking for one rather Untethered. Please give one with a tutorial!

There isn't one. So if you updated to iPhone 5 6.1.3 you can't jailbreak because iPhone 5 can't be downgraded to iOS 6.1.2 only older iPhones can. The 6.1.3 update just fixed the gaps that were used to create the 6.1.2 jailbreak. There won't be a new jailbreak made until iOS 7 most likely. Because the jailbreakers have a new gap to jailbreak with they don't want to use it and reveal it for such small updates though which is why they won't until iOS 7 now. Which should be shown at Apple's WWDC 2013 and released with iPhone 5s this fall. So if you haven't upgraded it stay on 6.1.2 and jailbreak with the evasion jailbreak if you did i'm sorry but now you'll have to wait until iOS 7.