Mitchell Garabedian, a Boston lawyer, held a news conference Tuesday outside the diocese's headquarters, The Times of Trenton reported. He said the five men were sexually abused by the Rev. Ronald Becker in the 1970s and 1980s at Incarnation Church in Ewing just outside Trenton.
"These individuals cannot get their childhoods back," Garabedian said. "Father Becker molested them and stole their childhoods."
The diocese has not admitted any wrongdoing.
Becker was removed from parish work in 1989 when he was accused of "inappropriate conduct" and removed from the priesthood in 2002. When he died in 2009, he was under investigation after his niece charged he continually molested her as a child.
Garabedian said the five men will each get $200,000.
Caroline Berg Eriksen: Soccer player's wife triggers debate with post-birth selfie
18-year-old elf alleges mall Santa pinched her buttocks on the job