Combine grapefruit, oranges, banana, and pineapple with juice in a large bowl. Cut 1 lime in half; cut one half into thin slices, and add to fruit mixture. Juice remaining limes, and add juice to fruit mixture. Discard rind and pulp. Stir in apple juice. Cover and refrigerate at least 2 hours.
Spoon fruit mixture into 8 stemmed dessert glasses. Top each with a scoop of desired sherbet. Serve immediately.