Answer
$x\approx-3.305$
Work Step by Step
$e^{-5-2x}=5 \qquad \color{blue}{\text{ ...apply ln(...) to both sides } }$
$\ln e^{-5-2x}=\ln 5 \qquad \color{blue}{\text{ ...apply } \log_{a}a^{x}=x}$
$-5-2x=\ln 5$
$-2x=\ln 5+5\qquad \color{blue}{\text{ ... } /\div(-2)}$
$x=\displaystyle \frac{\ln 5+5}{-2}$
$x\approx-3.305$
