The early-morning arrests in various parts of Germany on Wednesday were accompanied by searches at 13 properties, federal prosecutors said.
Four of those arrested - identified only as Benjamin H, Ben-Maxim H, Lenny M and Jason R, in line with German privacy rules - are suspected of membership in a domestic terror organisation.
The fifth, Jerome M, is accused of supporting the group.
Two of the arrested also are accused of attempted murder and aggravated arson.
All are between the ages of 14 and 18.
Prosecutors said they were also investigating three other people, ages 18 to 21, who are already in custody.
All the suspects are German citizens.
According to the prosecutors, the group was formed in mid-April 2024 or earlier.
They said its members saw themselves as the last resort to defend the "German nation" and aimed to bring about the collapse of Germany's democratic order, with attacks on homes for asylum-seekers and on facilities associated with the left-wing political spectrum.
Two of the suspects set a fire at a cultural centre in Altdobern in eastern Germany in October, prosecutors said, adding that several people living in the building at the time escaped injury only by chance.
In January, another two suspects allegedly broke a window at a home for asylum seekers in Schmolln and tried unsuccessfully to start a blaze by setting off fireworks.
They daubed the group's initials and slogans such as "Foreigners out", "Germany for the Germans" and "Nazi area", as well as swastikas, prosecutors said.
Also in January, three suspects allegedly planned an arson attack on a home for asylum seekers in Senftenberg, but it never came about because of the earlier arrests of two of the men.
Justice Minister Stefanie Hubig said it was "particularly shocking" that all of those arrested were minors at the time the group was allegedly founded.
"This is an alarm signal and it shows that right-wing extremist terrorism knows no age," Hubig said in a statement.
In a separate case a week ago, German authorities banned a far-right group called "Kingdom of Germany" as a threat to the country's democratic order and arrested four of its alleged leaders.
