Unlock iPhone 3.1.3 Baseband 05.11.07 With Blacksn0w RC2
As you are already aware, Blacksn0w, the unlock tool from Geohot, is unable to unlock iPhone 3G/3GS with firmware 3.1.3 on baseband 05.11.07. Fortunately, a hacker by the name MSFT Guy has provided a patch for Blacksn0w which fixes this issue. Manually applying this patch to Blacksn0w is not so easy, and Geohot has remained silent on this topic.
Thanks to the developer of PushFix (the first fix for push notifications on hacktivated iPhone before PushDoctor came along), we now have Blacksn0w RC2 Final version (1.0), patched version of Blacksnow which works with iPhone 3G/3GS firmware 3.1.3 on baseband 05.11.07. The final version of Blacksn0w RC2 fixes some bugs that were found in the earlier ‘test’ version, including a WiFi problem and the boot loop issue.
In order to unlock your iPhone 3.1.3 on baseband 05.11.07, go to Cydia, add the source http://cydia.pushfix.info. Then search for ‘Blacksn0w RC2’ in Cydia, and install it. After rebooting your iPhone, it is automatically unlocked and you can choose any carrier of your liking.
Note that Blacksn0w RC2 can only unlock iPhone 3.1.3 baseband 05.11.07; unlock for iPhone 3.1.3 baseband 05.12.01 is not yet available.

In order to install Cydia, you need to first jailbreak your iPhone or iPod Touch. For jailbreaking iPhone 3.1.3, you may use Sn0wbreeze (Windows only), redsn0w (Windows, Mac OSX), or PwnageTool (Mac OSX). Unlocking iPhone 3.1.3 can be done using either Blacksn0w or Ultrasn0wF0recast lets you check if your iPhone/iPod Touch is tethered or unlockable.