The 28-year-old has already admitted to killing two of the infants in an earlier unsolved case, police said.
She turned herself in after they took a DNA sample, and confessed to killing the children, who were born alive, they said.
Her identity has not been released in accordance with German privacy laws.
The case had been under investigation for years, after a newborn's body was found in a paper-recycling plant near the northern city of Flensburg in 2006.
A second body was found in a car park in 2007.
"She is also suspected of giving birth to three more children and subsequently killing them," police in the city of Flensburg said in a statement.
Three further bodies were found in the cellar of the woman's house, police said.
The woman was afraid her husband would leave her because he did not want any more children, prosecutor Ulrike Stahlmann-Liebelt told a news conference in Flensburg.
He knew nothing of the five births, she added.
The couple have two living children, aged eight and 10.
There have been several cases in recent years in Germany of women who have killed several of their own children.
In 2006, a woman was convicted of manslaughter and sentenced to the maximum 15 years in prison for killing eight of her newborn babies and burying them in flower pots and a fish tank in the garden of her parents' home near the German-Polish border.