Bring the peaches, sugar, and 1/2 cup water to a simmer over medium heat; remove from heat and let steep until completely cool. Transfer syrup and half the peaches (discard remaining peaches) to a food processor or blender and puree; strain through a fine mesh strainer, and refrigerate until cold.
Meanwhile, bring the remaining 4 cups water to a simmer over medium heat; then remove from heat, and add tea bags. Let steep for 1 minute, and remove tea bags. Let cool to room temperature, and then refrigerate until chilled. Stir the syrup and tea together in a 2-quart pitcher, and serve over ice.