In a statement the South African Police Service said they were summoned to a street at six in the morning where they discovered the bodies of four males and one female with gunshot wounds.
The deaths could be linked, police said, to another incident in the early hours of the day in which a person was shot and killed in the same vicinity.
Police have yet to identify the victims or the motive for the shooting.
South Africa has around 20,000 murders recorded each year out of a population of 60 million - one of the highest rates in the world.
