Cold brew the tea. Add the tea bags to a large (64 oz) mason jar or pitcher. Pour in the 5 cups of cold water and give a stir. Close the top and refrigerate for 12 - 24 hours.
The next day, cube about ¼ of a watermelon and add it to a blender (add roughly enough to produce 2 cups of watermelon juice). Pour in the pineapple juice and blend. Strain the juice into a container.
Remove the tea from the fridge and discard the tea bags.
Gently pour the watermelon pineapple juice into the tea. Juice 1 lime into the mixture. Give a good stir. Serve over ice and refrigerate the remaining.