Emma Poole, a police spokeswoman, says three males were found dead at the scene in the northwest neighbourhood of Brentwood.
Poole says the remaining two victims — a male and a female — died in hospital, and that all five appeared to be in their late teens or early 20s.
She says a man in his 20s was arrested with the help of the police canine unit about 40 minutes after the stabbing and that he was taken to hospital for treatment of dog bites.
There was no immediate word on charges against the suspect, or the possible motive for the stabbings.
Neighbours in the area say the house was being rented by University of Calgary students and that a so-called Bermuda shorts day party had started there on Monday.