In a Dutch oven, bring water to a boil. Remove from the heat; add tea bags. Cover and steep for 3-5 minutes. Discard tea bags. Stir in the limeade concentrate, sugar and rum.
Transfer to a 4-qt. freezer container; cool. Cover and freeze for 6 hours or overnight.
To use frozen limeade mixture: Combine the limeade mixture and soda in a 4-qt. pitcher. Or for 1 serving, combine 1/2 cup limeade mixture and 1/4 cup soda in a glass. If desired, garnish with lime slices. Serve immediately.