Stir together 1 1/2 cups water, sugar, and sliced peaches in a large pot. Bring to a simmer until the sugar is dissolved, the mixture becomes syrupy, and the syrup is infused with peach flavor. Set syrup aside to cool; strain off peaches and reserve them for another use.

In another pot, bring the remaining 4 cups water to a boil. Turn the heat off, add tea bags, and steep for 4-6 minutes. Remove and discard tea bags.