They were convicted in Texas of selling computer equipment to Libya and Syria, among other things. From the BBC, with thanks to Twostellas:
The men - Ghassan, Basman, Bayan, Hazim and Ihsan Elashi - ran a computer business in Richardson, Texas.
They were tried on more than 20 counts of money-laundering and false statements on export documents.
Three of the brothers are facing separate charges of funnelling money to the militant Palestinian group Hamas.
The five ran a firm called InfoCom.
On Wednesday, they were found guilty of shipping money to countries regarded by the US as sponsors of terrorism, and could face up to 10 years in jail.
During the trial, prosecutors said they repeatedly filed false export forms to deceive the authorities about the nature of their business.
The defence argued that the brothers did not knowingly break laws and that the equipment sent to the Middle East consisted only of low-grade computers.
UPDATE: Daniel Pipes (thanks to Mentat) notes that one of these men, Ghassan Elashi, was a founding board member of CAIR's Texas chapter. I am somewhat abashed at not noticing his name before Mentat pointed it out: just last week I was writing about Elashi and other CAIR officials who have been arrested on terrorism-related charges in a piece for my forthcoming essay collection, The Myth of Islamic Tolerance.