In a medium saucepan over low to medium heat, soften the peaches with ½ cup of the water. Cook until very soft. Lightly smash the fruit with a potato masher. Let the puree cool.
In a large saucepan or tea kettle, boil the remaining 4 cups of water. Use a large glass measuring cup to brew the tea bags with the boiling water. Stir in the sugar to dissolve. Let steep for 20-30 minutes. Pour the peach puree and brewed tea into a 1-gallon pouring pitcher and add enough ice to fill it to the top. Serve with additional ice and a garnish of fresh mint.