The first defendants from the April 16 immigration raid at the local Pilgrim's Pride chicken processing plant appeared before Federal Magistrate Susan Kerr Lee on Tuesday.
She ordered that all five of the men, who are citizens of Guatemala, continued to be detained.
They are all represented by the federal defender's office.
One man faces up to 10 years in federal prison, while those with only illegal re-entry charges face up to two years.
Roberto Gabriel-Ramirez, 40, said he has a third-grade education. He is charged with illegal re-entry into the country and use of a fraudulent Social Security card.
Andres Loarca-Reynoso, 33, who said he went to school for only one year, faces similar charges.
Their trials were set for early July.
Jose Luis Ramirez-Vasquez, 26, said he had four years of education. He faces up to two years for illegal re-entry.
A man listed as Jean Luis Dardon-Canelo said his real name is Jose Luis Dardon-Canelo. Age 23, he had nine years of schooling.
Alfred Gabriel-Torres said his real last name is Tomas. He is 35 and has three years of education.