Laplace II: Steps, Impulses & Convolution · Superchallenge problem

Let $g(t)=u(t)-u(t-1)$ (the unit box on $[0,1)$) and let $g^{*5}=g*g*g*g*g$. Using $\mathcal{L}\{g^{*5}\}=\left(\dfrac{1-e^{-s}}{s}\right)^5$, find the maximum value of $g^{*5}(t)$.