Richard Klugh, one of the lawyers, told a panel of three judges: "The court should find that the defendants were prejudiced [by what the prosecution said] and the court should grant a new trial."
The five - Gerardo Hernandez, Ramon Labanino, Rene Gonzalez, Antonio Guerrero and Fernando Gonzalez - were sent to Florida by the government of Fidel Castro.
There they gathered information about anti-communist exile groups and sent it back to Cuba using encrypted software, high-frequency radio transmissions and coded electronic telephone messages.
All five were convicted of being unregistered foreign agents, and three were found guilty of espionage conspiracy for failed efforts to obtain military secrets.
They were given prison sentences ranging from 10 years to life in December 2001, but the case has been through a range of appeals and before several courts since.
Monday's hearing was the third time the politically charged case has come before the US court of appeal, and a crowd of dozens lined up outside the Atlanta courthouse more than two hours before the arguments began.
The Cuban Five are celebrated at home as national heroes victimised by Washington as part of its diplomatic campaign against Cuba.
But to many members of the Cuban exile community they were justly convicted and Havana's support for the men is seen as an example of Cuba's pursuit of its own anti-US agenda.
Government lawyers refuted an argument from the defence that its case was "over-hyperbolic" and said there was no misconduct by the prosecution at the 2001 trial.
"This was a soberly tried case. It was squarely based on evidence... The government did not exploit red-baiting in this case," government lawyer Caroline Heck Miller told the court.
'Inference upon inference'
She was referring to claims by the defence that prosecutors unfairly characterised conviction of the men as of national importance because they represented a communist government opposed to the US.
One of the men, Gerardo Hernandez, was also indicted for conspiracy to commit murder based on the allegation that he passed information to Havana that led to the downing in 1996 by a Cuban MiG jet of two small aircraft operated by a Miami-based Cuban exile group and flying near Cuba. Four people were killed.
Hernandez was sentenced to two life terms, Antonio Guerrero and Ramon Labanino got life, Fernando Gonzalez received 19 years in jail and Rene Gonzalez got 15 years.
Hernandez says he was spying on paramilitary exile groups in Miami, not on the US itself, when he and four members of his so-called Wasp Network were arrested.
The mission was to prevent "terrorist" attacks on Cuba, according to Ramsey Clark, a former US attorney general who was present in support of the men.
"There is an injustice in this case... The theory that the government used [to prosecute Hernandez] is a classic pile of inference upon inference upon inference," Klugh said.
The three judges at the court of appeal in Atlanta may take many weeks to make a ruling in the case, supporters of the men said.