The target of the plot was a bridge that carries a four-lane highway over part of the Cuyahoga Valley National Park in the Brecksville area, about 15 miles south of downtown Cleveland, the FBI said.
Authorities said three of the men were arrested Monday and are self-described anarchists, not tied to international terrorism.
It wasn't immediately clear whether the men had attorneys. All of the suspects, ranging in age from 20 to 35, were expected to appear in federal court Tuesday afternoon.
The FBI said three were arrested on charges of conspiracy and trying to use explosives to damage property affecting interstate commerce. They were identified as Brandon L. Baxter, 20; Douglas L. Wright, 26; and Anthony Hayne, 35. Their hometowns were not provided.
Charges were pending against the other two men.
Baxter, Wright and Hayne considered different plots over several months, including distracting law enforcement with smoke grenades while trying to bring down financial institution signs in downtown Cleveland, federal authorities alleged. The defendants' finally settled on blowing up the bridge, authorities said.
"The individuals charged in this plot were intent on using violence to express their ideological views," Special Agent Stephen D. Anthony, who oversees the FBI's Cleveland division, said in a statement. "The Joint Terrorism Task Force will continue to be vigilant in its efforts to detect and disrupt any terrorism threat, domestic or international."
Associated Press writers Pete Yost in Washington and Kantele Franko in Columbus, Ohio, contributed to this report.