Answer
$x=-\dfrac{\ln10}{5}\approx-0.460517$
Work Step by Step
$e^{-5x}=10$
Apply $\ln$ to both sides of the equation:
$\ln e^{-5x}=\ln10$
The exponent $-5x$ can be taken down to multiply in front of the $\ln$:
$-5x\ln e=\ln10$
Since $\ln e=1$, we are only left with:
$-5x=\ln10$
Solve for $x$:
$x=-\dfrac{\ln10}{5}\approx-0.460517$
