Monthly Salaries of Five VPs

Let the 5 integer salaries in ascending order be $x_1, x_2, x_3, x_4, x_5$. Median = 5 $\implies x_3 = 5$. Only mode = 8 $\implies x_4 = x_5 = 8$. Mean = 5 $\implies x_1 + x_2 + 5 + 8 + 8 = 25 \implies x_1 + x_2 = 4$. Since all are integers and mode is uniquely 8, $x_1$ and $x_2$ must be distinct positive integers less than 5. So $x_1 = 1, x_2 = 3$. Highest = 8, Lowest = 1. Sum = $1 + 8 = 9$.