trying to upgrade 3gs from 4.3.5 - 5.1.1

kjf

I tried to jailbreak the 4.3.5 with no success. So i was wondering if i download 5.1.1 firmware, connect my phone and in itunes hold shift and click restore (windows machine ). Can i choose the firmware file that i downloaded and update it that way? If this doesnt work is there any other way to upgrade to 5.1.1 instead of going to 6.0 and downgrading.