After more than 15 years covering everything Apple, it’s with a heavy heart we announce that we will no longer be publishing new content on iMore and the iMore forums will be closing as of November 1st, 2024.
The baseband for 3.1.3 is 5.12, not 5.11. 5.11 is from 3.1.2, and if you're running 5.11 on 3.1.3, it's because you upgraded to 3.1.3 by using either sn0wbreeze/PwnageTool.
You just use sn0w/blacksn0w to unlock 5.11. It's that simple.
Seriously, there is no real rush to jailbreak, is there? I upgraded to 3.1.3, and I'm just waiting to jailbreak. Albeit, I've heard that Apple are trying to band people that are jailbroken to access the 'app store'.