The extension of Theorem on the forbidden graphs $\overline{K}_3$ and $C_5$

Let $\mathrm{er}_{s}(\{\overline{K}_3,C_5\})$ denote the minimum asymptotic density of $s$-cliques among graphs avoiding both $\overline{K}_3$ and $C_5$. Theorem's extension conjecture. The conclusions of the theorem concerning $\{\overline{K}_3,C_5\}$, in particular

$$\mathrm{er}_{s}(\{\overline{K}_3,C_5\})=2^{1-s},$$

hold for every $s\geq 7$. The paper does not pursue the proof of this extension; it would remove the stated restriction on $s$ in the theorem.