\(\left(x+5\right)^8=9\left(x+5\right)^6\Leftrightarrow\left(x+5\right)^8-9\left(x+5\right)^6=0\)
\(\Leftrightarrow\left(x+5\right)^6\left[\left(x+5\right)^2-9\right]=0\Leftrightarrow\left(x+5\right)^6\left(x+2\right)\left(x+8\right)=0\Leftrightarrow x=-5;x=-2;x=-8\)