The necessary information's are already given in the question. Based on those information's the answer to the question can be easily determined.
Amount of water recirculated by the pump in 1/5 of an hour = 60 gallons
we already know
1/5 of an hour = (1/5) * 60 minutes
= 12 minutes
Then
Amount of water recirculated by
the pump in 60 minutes = (60/12) * 60 gallons
= 5 * 60 gallons
= 300 gallons
So the amount of water recirculated by the pump per hour is 300 gallons.