Go to Settings / General / Software Update is there a newer version to install?
I'm afraid if it does not offer you an older version in the App Store when you try to download it then that means Pandora is not supporting iOS 5.1.1 sorry. If you had a working version installed previously you can try to recover the backup for that
Have iTunes open, .
Download EasyFind at https://www.macupdate.com/app/mac/11076/easyfind and search for .ipa on your entire hard drive. Sort by name and go to Pandora section.
Double click on the version you find and it will ask if you want to replace Pandora app with older version. Say yes and then sync your iPod Touch and it might work.