 Solution

A connected Feynman diagram that is a cubic tree with five external legs has three vertices and two internal lines. Its unique unlabeled topology is a chain: two external legs meet at each end vertex and one external leg attaches to the middle vertex. The five-point tree amplitude in phi cubed theory therefore has fifteen labeled tree-level Feynman diagrams: choose the middle external leg in five ways, then partition the remaining four legs into two unordered pairs in three ways.