$\begin{array}{l}
\left( {m - 1} \right)\sin 5x + \left( {m - 6} \right)cos5x = 19 - m\\
Vô\,nghiệm \Leftrightarrow {\left( {m - 1} \right)^2} + {\left( {m - 6} \right)^2} < {\left( {19 - m} \right)^2}\\
\Rightarrow {m^2} - 2m + 1 + {m^2} - 12m + 36 < {m^2} - 38m + 361\\
\Rightarrow {m^2} + 24m - 324 < 0\\
\Rightarrow - 12 - 6\sqrt 3 < m < - 12 + 6\sqrt 3
\end{array}$