= Solution
There are
$$
\boxed{0\text{ fundamental five-gauge-boson vertices}.}
$$
For a <Yang-Mills theory>, schematically $F=\partial A+gAA$. The gauge kinetic <Lagrangian> is quadratic in $F$, so its terms are at most quartic in the <gauge fields>:
$$
F^2\sim(\partial A)^2+g(\partial A)AA+g^2AAAA.
$$
Thus there is no elementary five-leg pure-gauge <interaction vertex> in the renormalizable <Standard Model>. A five-boson scattering amplitude can still be assembled from several lower-valence vertices, or generated by <loop diagrams>. The number of external legs of a complete <Feynman diagram> is not the valence of a fundamental vertex.
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