Answer
See below
Work Step by Step
We are given that $F(s)=\frac{e^{-s}}{(s+1)(s-4)}$
Now,$f(t)= L^{-1}[\frac{e^{-s}}{(s+1)(s-4)}]\\
=L^{-1}[\frac{e^{-s}}{5}(\frac{1}{s-4}+\frac{1}{s+1})]\\
=\frac{1}{5}L^{-1}[L(e^{4t}-e^{-t})]\\
=\frac{1}{5}[u_1(t)(e^{4(t-1)}-e^{-(t-1)})]$
