Below is a walkthrough for the Capture the Fairy task in Rune Factory 5.
Client: Livia
Wanted: Fairy
Location: Phoros Woodlands (sighted in the Central Region)
Reward(s): Farming Bread x1
To start this request, speak with Livia in her office at the Silo and choose the I want to check the wanted monster list option. You’ll then want to select the Fairy wanted posted to begin the hunt. Make your way to the Phoros Woodlands east of Rigbarth then follow the path east. When you reach the split (past the southern path leading to the Whispering Woods) take the southeastern path and follow it until you come to a wooden bridge. Cross the bridge the head off to the left (going northeast) to find a pond. The Fairy can be found somewhere around this pond. You going to want to put some pressure on her with physical attacks to whittle her health down low enough to capture her. Watch out for her wind attack as it can deal massive damage and even one-shot those who are too low a level. After catching the Fairy, return to Livia in the Silo to complete the task and receive your reward.
*Fairy map location