$\begin{array}{l}
y' = 6{x^2} - 6x\\
y' = 0 \Leftrightarrow \left[ \begin{array}{l}
x = 0\\
x = 1
\end{array} \right.\\
f\left( 0 \right) = m,f\left( 1 \right) = m - 1,f\left( { - 5} \right) =  - 325 + m\\
 \Rightarrow f\left( 0 \right) > f\left( 1 \right) > f\left( { - 5} \right)\\
 \Rightarrow \mathop {\max }\limits_{\left[ { - 5;1} \right]} f\left( x \right) = f\left( 0 \right) = m\\
GT:\mathop {\max }\limits_{\left[ { - 5;1} \right]} f\left( x \right) = 7 \Leftrightarrow f\left( 0 \right) = 7 \Leftrightarrow m = 7\\
 \to A
\end{array}$