I wanted to know the best way to upgrade my baseband 5.11.07 to 5.13.04. It is an iPhone 3GS running iOS 4.1. The phone is jailbroken and unlocked. Also have shsh for 3.0, 3.1, 3.12, 3.13, 4.0, 4.01, 4.1, 4.21+, 4.34, 4.35. I've been trying to find a guide but no luck. Thanks in advance.
Is there a particular reason why you want to do this? AFAIK it wouldn't make much of a difference if any.
If you're insistent on doing it though, since you have SHSHs for 4.0.1, you'd want to run the TSS Server in TinyUmbrella and restore to a STOCK 4.0.1 firmware. That will put your baseband at 5.13.04 which is the default bb on stock 4.0.1.
If you would then like to restore back up to 4.1 or 4.2.1, create a custom firmware for it, run the TSS Server, and shift/option + restore to the cFW to preserve that baseband.