The 48-year-old woman, who conceived naturally, gave birth to two boys and three girls on Monday at Monash Medical Centre, Victoria.
But tragically, one of the girls has died, Seven Network reported.
A spokesman for Monash Medical Centre confirmed that four babies were delivered healthy.
''One unfortunately did not make it. Mum is doing well," he said.
The babies were delivered by Caesarean section by a team of 30 specialists. The family do not want to be identified.
The chance of conceiving quintuplets naturally is about one in 55 million, doctors say.