Enter GC5. You should receive a message about wailing screams notifying you of the presence of the Enner Beast. If you can't immediately see him anywhere, read the scroll of detect material and search for "enner beast flesh". This will reveal his location and help you in killing him as soon as possible. Press 'u' to toggle running on and sprint towards him. You should attempt to have a straight line of sight to him to be able to zap him with a fireball. If you can, teleport with telecontrol to be faster. When your health reaches bright red, quickly drink a can of healing liquid and continue searching.
Once you have the opportunity to blast him, do it. He's rather frail physically, and 2-3 direct fireballs should be enough to take him down. Do not use wands of striking, as they are less effective than fireballs against foes without armor. If everything went well, you should now be a proud owner of an enner beast corpse. Pick up the horn of fear he carries if you don't have one yet and explore the rest of the level as normal. Don't forget to get the things you left on GC4.
===GC6: The zombie level===