Three hours is a bit much Id say 2-2.5 should be fine. You will have a security line, and then check in but there should be a premium line for check in. 5AM is actually the beginning of the busy time for the airport since 5-8 am is when most flights are leaving to make mid day connections in Europe, but you are at the beginning of the parade of the bleary eyed. With the new airport -several years ago - planes are boarded via jetway vs buses driven out to the planes so it can be a hike out to the gates