Constrained Ramsey numbers for rainbow $P_5$

For any graph $H$, let $R_k(H)$ denote the minimum integer $n$ such that in every $k$-edge-coloring of $K_{n}$, there is a monochromatic copy of $H$. Given two graphs $H$ and $G$, the \emph{constrained Ramsey number} $f(H,G)$ is the minimum integer $n$ such that in every edge-coloring of $K_{n}$ wit