Bài giải:

${{\log }_{3}}\left( {{x}^{2}}-x-5 \right)={{\log }_{3}}\left( 2x+5 \right)$

$\Leftrightarrow \left\{ \begin{align}& 2\text{x}+5>0 \\ & {{x}^{2}}-x-5=2x+5 \\ \end{align} \right.$

$\Leftrightarrow \left\{ \begin{align} & 2\text{x}+5>0 \\ & {{x}^{2}}-3x-10=0 \\ \end{align} \right.$

 $\Leftrightarrow \left\{ \begin{align}& x>-\frac{5}{2} \\ & x=5\vee x=-2 \\ \end{align} \right.$

$\Leftrightarrow \left[ \begin{align}& x=5 \\ & x=-2 \\ \end{align} \right.$