You can now download and install BlackSn0w RC2 to unlock your iPhone 3.1.3 with baseband 05.11.07. The app should be available in the MMI repo soon, but if you can’t wait, you can always add this repo: http://cydia.pushfix.info/
After jailbreaking your iPhone, simply launch Cydia and look for BlackSn0w RC2. Download and install, then reboot your iPhone. You should be good to go.
Note that if you accidentally updated your iPhone to 3.1.3, thus updating your baseband to 05.12.01, you will not be able to use this hack.
To date there is still now jailbreak and unlock for iPhone 3.1.3 on baseband 05.12.01.