What turned the tide decisively in favor of the elves, men, and dwarves in the Battle of the Five Armies?

The arrival of the Eagles and Beorn changed the tide of the Battle of the Five Armies in favor of the Free peoples.
Though the battle started off promisingly, soon the Free peoples were under siege by the enemy forces. When things seemed like they might be hopeless, the Great Eagles of Misty Mountain arrived to lend their assistance to the Free peoples. The Eagles are intelligent creatures who were designed to be the messengers of the King of the Valar. They are enemies of any evil.
After the Eagles joined the fight, Beorn appeared as well. Beorn was a skin-changer who could change into different shapes. In this battle, he picked the shape of a bear. As such, he was able to kill the leader of the goblins, which effectively ended the battle as lesser goblins and wargs were killed by the Free peoples.