Manufacturers claimed horsepower ratings are usually inaccurate.  Often the rating stated is the peak HP.  Peak HP is achieved in an ideal situation for just a fraction of a second when the motor is started.  This vacuum has 5.0 HP in big, bold letters, with the word PEAK in small font.

If you look more closely, you will learn that the vacuum runs on 120 volts (V) and draws 10.0 amps (A).  From this, we can calculate a more realistic HP rating.

Amps x Volts = Watts —————————-> 10.0 x 120 = 1200
746 Watts = 1HP —–> Watts ÷ 746 = HP —–> 1200 ÷ 746 = 1.6
Now, this calculation thusfar assumes that the motor is 100% efficient, which none are.  70% efficiency is in the ballpark.  So…
HP x 70% = Realistic HP ————————> 1.6 x 70% = 1.1 HP