The operatives were arrested in southern Florida in 1998 and charged with "conspiracy to gather and deliver defense information to aid a foreign government, that is, the Republic of Cuba," the Web site killinghope.org reported.
They were also charged with failing to register as agents of a foreign government.
The five did not deny their operations, saying they were spying on anti-Castro Cuban exiles in the United States who they alleged were carrying out terrorist activities against Cuba.
After a trial in 2000, three were sentenced to life terms; the two others received sentences of 19 and 15 years.
The relatives made their plea to Global Exchange, a U.S.-Cuba solidarity group promoting exchanges and visits with representatives of both countries, Cuba's Communist Party newspaper Granma said.