In large heatproof bowl, pour 4 cups of the boiling water over tea bags. Let stand 10 minutes; discard tea bags.
In small microwavable bowl, mix remaining 1/2 cup boiling water, the sugar and vanilla. Microwave uncovered on High 1 minute, stirring until sugar is dissolved. Cool 5 minutes. Stir sugar syrup, orange juice and lime juice into tea; refrigerate 1 hour.
Serve over ice. Garnish with lime slices.