The men got sentences of up to six years for their activities on behalf of rebels who fought for an independent homeland for Tamils in Sri Lanka.
Prosecutors said the men extorted millions of euros from the Tamil diaspora through blackmail and threats.
But the defence counsel for the five men argued that they were freedom fighters.
In a complex ruling, the judge said the men were not convicted of supporting terror but that he found them guilty of involvement in a criminal organisation.
The Liberation Tigers of Tamil Eelam [LTTE] was outlawed by the European Union in 2006.
They fought a decades-long and bloody war against Sri Lankan authorities for a separate Tamil homeland in the north and east of the country, but were defeated by the Sri Lankan army in 2009.
Prosecutors also accused the men of "brainwashing" children by teaching them to make pictures of bombs and grenades.
This case is one of a number of prosecutions concerning both sides of the Sri Lankan conflict that are currently being considered in foreign courts.
A Dutch court has convicted five Dutch ethnic Tamil men for raising funds for the banned Tamil Tiger rebels.