  A $(p, q)$-coloring of $K_n$ is a coloring of the edges of $K_n$ such that
every $p$-clique has at least $q$ distinct colors among its edges. The
generalized Ramsey number $f(n, p, q)$ is the minimum number of colors such
that $K_n$ has a $(p, q)$-coloring. Gomez-Leos, Heath, Parker, Schweider and
Zerbib recently proved $f(n, 5, 8) \ge \frac 67 (n-1)$. Here we prove an
asymptotically matching upper bound.
