The origin of Sri Panchamukha Hanuman can be traced to a story in the Ramayana. During the war between Lord Ram and Ravana, Ravana took the help of Mahiravana who was the king of pathala.
Lord Hanuman in order to protect Lord Ram and Lakshman formed a fortress with his tail. But Mahiravana took the form of Vibeeshana and took Lord Ram and Lakshman to pathala loka.
Hanuman entered pathala loka in search of Rama and Lakshmana.He found out that to kill Mahiravana he had to extinguish 5 lamps at the same time. So he took the Panchamukha form with Hanuman, Hayagriva, Narasimha, Garuda and Varaha faces and extinguished the lamps. Mahiravana was killed immediately.
The story apart, Sri Panchamukha Hanuman was the upasana deity of Sri Ragavendra Tirtha, the saint of Mantralaya. The place where he meditated on Panchamukha Hanuman is now known as Panchamukhi, wherein a temple for Panchamukha Hanuman has been built.