Answer
$P_i=4.20hp$
Work Step by Step
We can determine the required power input as follows:
$\epsilon=\frac{Power\space output}{power \space input}$
This can be rearranged as:
$Power\space input=\frac{Power\space output}{\epsilon}$
$Power\space input=\frac{Fv}{\epsilon}$
We plug in the known values to obtain:
$Power\space input=\frac{(300)(5)}{0.65}$
$\implies Power\space input=2307.7lb\cdot ft/s=4.20hp$
