A birthday cake is to have two layers of cake separated by a layer of icing, with another layer of icing on top. There are 5 kinds of cake the chef knows how to make, and she may use either two different kinds or the same one twice for the two cake layers. The chef knows recipes for 3 different icings, and she will use two different recipes, one for each icing layer, in this cake. How many different cakes could the chef make? Note that the order of the layers matters, e.g. chocolate over strawberry is different from strawberry over chocolate.

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