Answer
$x =\dfrac{(\ln{8})-5}{2}$
Work Step by Step
Take the natural logarithm of both sides to obtain:
$\ln{e^{2x+5}} = \ln{8}$
RECALL:
$\ln{e^a} = a$
Use the rule above to obtain:
$2x+5=\ln{8}$
Subtract by $5$ on both sides of the equation to obtain:
$\begin{array}{ccc}
&2x+5 -5 &= &\ln{8}-5
\\&2x &= &\ln{8}-5
\end{array}$
Divide by $2$ on both sides of the equation to obtain:
$x =\dfrac{\ln{8}-5}{2}$