To prepare cake, line the bottom of a 15 x 10-inch jelly roll pan with wax paper.
Lightly spoon flour into a dry measuring cup; level with a knife. Combine flour, 6 tablespoons granulated sugar, and five-spice powder, stirring with a whisk.
Place egg whites in a large bowl; beat with a mixer at high speed until foamy. Add cream of tartar and salt, and beat until soft peaks form. Add 6 tablespoons granulated sugar, 2 tablespoons at a time, beating until stiff peaks form. Beat in juice and extracts.
Sift 1/4 cup flour mixture over egg white mixture; fold in. Repeat procedure with remaining flour mixture, 1/4 cup at a time. Spread batter into prepared pan. Sprinkle with 1/3 cup coconut. Bake at 325° for 20 minutes or until cake springs back when lightly touched.
Place a clean dish towel over a large wire rack; dust with powdered sugar. Loosen cake from sides of pan; turn out onto towel. Carefully peel off wax paper; cool for 3 minutes. Starting at narrow end, roll up cake and towel together. Place, seam side down, on wire rack; cool cake completely. Unroll cake, and remove towel. Spread sorbet over cake, leaving a 1/2-inch border around outside edges. Reroll cake. Wrap cake in plastic wrap; freeze 1 hour or until firm.
To prepare compote, combine mango, pineapple, kiwi, brown sugar, and rum, and let stand 20 minutes. Cut cake into 16 slices, and place 2 slices on each of 8 plates. Spoon about 1/4 cup compote over each serving, and sprinkle each serving with 1 1/2 teaspoons toasted coconut.