In Wutai there is a Pagoda in the North of the town called the Pagoda of the Five Mighty Gods.
Only those born in Wutai can complete and must face the battles 1-on-1.
After recruiting Yuffie, visit the town and head to north Wutai and enter the Pagoda.
Below are all 5 fights, with tips on beating them.
Make sure to have enough equipment and items as you may need to restore HP/MP between battles and make adjustments to your equipment before each fight.
When you finish a battle, head up the stairs to the next.