Dip the rim of tall glasses into the egg whites, and then the sugar. Put the rum, Triple Sec, and juices into a cocktail shaker. Shake to mix. Fill the glasses with the ice and pour the cocktail over it. Decorate with cherries, pineapple, and/or orange slices, and drink with a straw.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.