The babies, born Friday morning, join the Derricos' 7-year-old daughter, 3-year-old son and 1-year-old twin boys. All of the children's names begin with the letter "D."
He said the prospect of caring for such a large family occasionally causes him anxiety, but he says he's ready.
"To go from four for nine, that's a level of preparation that requires you be a billionaire," Deon Derrico said. "But whatever has to be done to take care of my children, I'm going to do it."
The infants were delivered at Banner Desert Medical Center in Mesa, under the supervision of Dr. John Elliott, who specializes in multiple births.
Elliott did not respond to a call seeking comment.
Evonne Derrico was not immediately available for comment.
Deon Derrico, 42, who works as a property manager for a real estate company, said friends have already volunteered to help babysit.
The family lives in a 2,900-square-foot, five-bedroom home. They plan to turn their home-theater room into a nursery. Deon Derrico said he needs to figure out what kind of vehicle the family should have; their minivan won't be big enough to move everyone around at once.
The couple initially thought they would be having quadruplets, but found a fifth baby in the womb on a later exam.
Deon Derrico said the couple conceived without fertility drugs. But they have gone through four miscarriages, and Evonne Derrico had been prescribed hormones to help maintain the pregnancy to term, Deon Derrico said.
"God is good," he said. "He gave us all those four back plus one on schedule."
The family moved to Arizona after 22 weeks for specialized care. The infants are expected to remain in the hospital for several weeks before heading home for Las Vegas.
Deon Derrico said he and his wife have not ruled out having more children.
"We've always talked about between 11 and 12 children," he said, adding, "I want as many children as God will bless me with."