Rule of thumb, you need support for every 3-4 inches of cake. For a 5" inch high cake, it's best to make two (2) 2 1/2 inch high cakes with supports in the bottom. This is more important with dense cakes and less so with sponges. Just a rule of thumb, FWIW...
You can't ever have too much support...
Also think about how this cake will be served... For me, 3 layers would be 6" of cake + filling and frosting. That's going tobe an awkward shape to cut and serve.
I would make 4 layers out of the ame amount of batter. Layer 2 of them on a board and stack on top of the other 2 layers. Then when it is time to serve, you will have 2 cakes that are the same size/depth and you don;t have half of the people eatig cake with filling and half eating it without...
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