PLACE THE MANGO, BANANA, LIME JUICE, SUGAR SYRUP, AND RUM IN A BLENDER AND PROCESS UNTIL SMOOTH. ADD 2 CUPS OF ICE AND PROCESS AGAIN UNTIL SMOOTH AND THICK. SERVE ICE-COLD IN HIGHBALL GLASSES WITH THE MANGO SLICES.
*TO MAKE SIMPLE SYRUP, HEAT 1 CUP SUGAR AND 1 CUP WATER IN A SMALL SAUCEPAN UNTIL THE SUGAR DISSOLVES. CHILL.