On recognizability of some finite simple orthogonal groups by spectrum

It is proved that if $G$ is a finite group with the same set of element orders as simple group $D_p(q)$, where $p$ is a prime, $p\ge5$ and $q\in\{2,3,5\}$, then the commutator group of $G/F(G)$ is isomorphic to $D_p(q)$, the subgroup $F(G)$ is equal to 1 for $q=5$ and to $O_q(G)$ for $q\in\{2,3\}$, $F(G)\le G'$ and $|G/G'|\le2$.