Place a small plate in the freezer. Transfer the peach mixture to a large, heavy pot. Add 4 of the tea bags, and crumble the contents of the 5th tea bag over the peaches. Bring to a boil, and cook, stirring gently, for 15-20 minutes. Remove the tea bags and discard. Check the preserves for doneness by spooning a small amount onto the plate from the freezer. Tilt the plate, and if the jam doesn't run, it's done (if it does, cook for a few more minutes until it thickens up a bit.) Skim any foam from the surface of the jam, then ladle into 4 clean, hot pint jars. Wipe the rims with a damp towel, then seal and process for 10 minutes in a boiling water bath.