Let $X$ be the waiting time and $F_{X}(x)$ be the CDF. Then, \begin{align} F_{X}(x) = \begin{cases} 0 &\mbox{ $x < 0$}\newline \frac{2}{3} &\mbox{ $x = 0$}\newline \frac{2}{3} + \frac{1}{30}x &\mbox{ $0 < x < 5$}\newline 1 &\mbox{ $5 \leq x$} \end{cases} \end{align} The PDF is simply the derivate of the CDF. Thus, expectation is \begin{align} E[X] = \frac{2}{3}(0) + \int_{0}^{5} \frac{1}{30}x dx + \frac{1}{6}(5) = \frac{5}{4} mins \end{align}