I want to jailbreak my iPhone 5, but I have iOS 6.1.3

I can't find a program that will jailbreak iOS 6.1.3, the one I have tried needs passwords!

Your out of luck. There's no jailbreak for ios 6.1.3. There probably won't be a jailbreak again til after ios 7. And there's no telling how long it will take them to jailbreak it.