Preheat the oven to the temperature called for in the cake mix instructions. Lightly grease five 8-inch cake pans and dust with flour, tapping out excess flour.
Place the ground bananas, blueberries, mangos, peas and raspberries in separate medium mixing bowls.
Prepare the cake mix batter according to package instructions, using the eggs, egg whites and oil. Divide the batter among the five mixing bowls. To the raspberry batter, add 4 drops red food coloring. To the mango batter, add 1 scant drop red and 3 drops yellow food coloring. To the banana batter, add 4 drops yellow food coloring. To the green pea batter, add 3 drops green food coloring. To the blueberry batter, add 3 drops blue food coloring. Mix each bowl of batter until well combined and uniform in color.
Scrape the batters into the prepared cake pans. Bake in batches (3 pans in the first batch, 2 pans in the second), rotating the pans halfway through the baking time, until a toothpick inserted in the center comes out clean, 20 to 25 minutes. Remove from the oven; when cool enough to handle, turn the cakes out onto a wire rack to cool completely.
To assemble the cake, place the blue cake layer onto a cake platter and spread the top with 1/3 cup frosting in an even layer. Top with the green layer and spread with 1/3 cup frosting. Repeat with the yellow, orange and red layers until you have stacked all the layers. Frost the sides and top of the cake in an even layer. Use the reserved bananas, blueberries, mangos, peas and raspberries to decorate the top of the cake in a rainbow pattern. Any remaining fruit can be crushed lightly, mixed together and used to decorate the sides of the cake.
Use a food processor to finely grind the frieze-dried fruit and peas.