Preheat oven to 325 degrees F (165 degrees C). Grease a 10 inch tube pan. In a small bowl, combine flour and baking powder. Set aside. In a measuring cup, combine the milk and 1 teaspoon each coconut, lemon, rum, butter and vanilla extracts; set aside.
In a large mixing bowl, cream butter, shortening and 3 cups sugar until light and fluffy. Add eggs, and beat until smooth. Beat in flour mixture alternately with milk mixture, beginning and ending with flour mixture. Spoon mixture into prepared pan.
Bake for 1 1/2 to 1 3/4 hours, or until cake tests done. Cool in pan on wire rack for 10 minutes.
Turn cake out of pan onto wire rack. Place waxed paper under rack to catch glaze drippings. Slowly spoon Five Flavor Glaze onto top of hot cake. Cool completely.
To make the Five Flavor Glaze: In a saucepan, combine 1/2 cup sugar, water and 1/2 teaspoon each coconut, lemon, rum, butter and vanilla extracts. Bring to a boil, stirring until sugar is dissolved.