Absinthe 2.04 works on *all 5.1.1* devices. If the device has iOS 5.1.1....Then it will work.
I personally recommend redsn0w. It is faster then Absinthe for some reason.
Just long as you do as the above poster said...Restore device, setup as new device and NOT from backup, then you should be good.
This is what i would do.
Before restoring:
Transfer purchases to iTunes, right click on devices name in iTunes and click "Transfer Purchases".
make sure Contacts is toggled on in Settings> iCloud. (also make sure that no other email account has Contacts toggled on. You will want to make sure you choose to "Use iCloud" when you setup the phone, and when you add more email accounts, if any, make sure that you toggle Contacts off". Only iCloud should have contacts toggled on, which is automatically enabled when you choose "Use iCloud" when setting up the phone after restore)
Anything toggled on in Settings> iCloud will be restored back to your phone even if you setup as new device.
Restore:
Restore in iTunes to 5.1.1, be sure to setup as new device and NOT from backup. After restore, follow the initial on screen setup until you get to the SpringBoard(home screen). Don't do "anything" once you can see the SpringBoard.
In iTunes, choose "setup as new device" click Next.
Make sure "Automatically sync apps" is *unchecked*.
Click done.
Let iTunes download Safari safe browsing data...wait til its done.
Close iTunes.
Open redsn0w, which you can get it from here:
Dev-Team Blog
Click the jailbreak button.
Do not touch your device until the phone reboots, and then resprings after it has rebooted.
After that, your done.
now sync music, tones, videos, etc. Download apps from the AppStore instead of syncing them from iTunes. dont have to, but I think it makes the jailbreak more stable.
After that you can open Cydia. let it load completely before doing anything. Might wnat to set autolock to "Never' before opening Cydia.
Once Cydia is fully loaded, you can start installing tweaks n stuff. I recommend you search and install Mobile Substrate first before anything.
Be *EXTREMELY CAREFUL* in Manage> Packages. If you uninstall the wrong package(like a package that will remove "Cydia Installer"), then you will be screwed and you will have to restore.
Every time you go to uninstall a package, check the list to make sure that "Cydia Installer" or "Mobile Substrate" is NOT on the list. But that is for future reference.
Do not install *anything* that does not specifically say that it is iOS 5.1 compatible in the packages description.
Its all common sense really, but mistakes happen. All that is needed to enjoy a nice stable jailbroken device is common sense and *paying attention* to what you are doing. That is all.
Enjoy.