Police authorities say the incident happened on Wednesday morning, "at around 06:00 (0400GMT)" in Ncumu Street.
"Police were summoned to a shooting incident in Ncumu Street where the bodies of four males and one female were discovered with gunshot wounds," read a statement released by the South African Police Service, SAPS.
SAPS said the deaths could be linked to an incident in the early hours of the day where another person was shot and killed in the same vicinity.
The victims of the shootings are yet to be identified.
The shootings in Western Cape happened soon after the murder of Luke Fleurs, a South African footballer and celebrity who was shot dead by robbers in Johannesburg early this month.
Experts say the nation continues to suffer from extremely high crime rates — a key political issue ahead of general elections in May, with opposition parties pointing to the government's perceived failure.
Official figures show that South Africa recorded almost 84 murders a day between October and December.
Information for this article was sourced from Reuters and Agence France-Presse.