The rate at which the hotel housekeeper is cleaning is 5/1 of the first floor per hour.
To calculate how many floors she cleans in an hour, divide the total number of floors cleaned by the cleaning time: 5 / 3 floors/hour = 1 / 3 floors / (1 / 5 hours).
She thus cleans five floors in an hour.
Convert the mixed number to a fraction in order to represent this as a fraction:
5 / 3 = (5 * 3) / 3 = 15 / 3 = 5/1.
Therefore, the rate at which the hotel housekeeper is cleaning is 5/1 of the first floor per hour.