On finite nonsolvable $5$-primary groups with disconnected Gruenberg–Kegel graph such that $\bigl|\pi\bigl(G / F(G)\bigr)\bigr| \le 4$

This paper describes the chief factors of the commutator subgroups of finite nonsolvable groups $G$ with disconnected Gruenberg–Kegel graph having exactly $5$ vertices in the case where $G / F(G)$ is an almost simple $n$-primary group for $n \le 4$.