The oxidation state of $\mathrm{Cr}$ in ${\mathrm{CrO}}_5$ is

In ${\mathrm{CrO}}_5$​, one oxygen is attached to $\mathrm{Cr}$ through the double bond. It has oxidation number $-2$. Four oxygen atoms are attached to $\mathrm{Cr}$ atom through a single bond. Each of these oxygen atoms possess oxidation number $-1$.

Let $\mathrm{x}$ be the oxidation number of chromium. The net charge on ${\mathrm{CrO}}_5$ is zero.

Hence, 

$$\begin{gathered} \mathrm{x}-2+4\left(-1\right) = 0 \\ \mathrm{x} = +6 \end{gathered}$$