People queue up for Covid-19 testing in Melbourne on May 12, 2021.
Photo: AFP / William West
Three of them are close family contacts of the initial case, whose source of infection remains unknown.
The first case was a man who showed symptoms of the coronavirus on 20 May. He got tested two days later on 23 May.
A male relative went with him when he got tested, and that person - who was not showing symptoms - had also tested positive, Foley said.
Both live in Whittlesea, in Melbourne's outer north.
Two other relatives, a woman and a preschool-aged child, were also tested and returned positive results.