In a small pot, steep the tea bags in 1 cup of boiling water for 5 minutes.
Remove the tea bags and mix in the honey until dissolved. Stir in the orange, lemon and lime juice along with the remaining 4 cups of water.
Chill the tea mixture for at least 3-4 hours to get thoroughly cold.
In a large pitcher, add in a good amount of ice, followed by the tea mixture, along with any citrus slices if using.
Smack the mint lightly to release the fragrant oils. Divide the mint in half and remove the leaves from the stems from one portion. Add the mint leaves to the tea mixture and top with the lemon-lime soda.
To serve, pour the punch into chilled glasses and garnish with a sprig of the remaining mint.