Sea $u=\sqrt{\exp(-3x)}\implies du=\dfrac{-3\exp(-3x)}{2\sqrt{\exp(-3x)}}dx=-\dfrac{3}{2}\sqrt{\exp(-3x)}dx$.
Luego, $\displaystyle\int5\sqrt{\exp(-3x)}dx=\displaystyle\int-\dfrac{10}{3}du=-\dfrac{10}{3}u+c=-\dfrac{10}{3}\sqrt{\exp(-3x)}+c$.