The University of Texas Southwestern Medical Center said Monday that the three boys and two girls are in stable condition.
Hospital officials say the youngsters were born premature Thursday to missionaries Carrie and Gavin Jones.
The quintuplets have been named Will Edward, David Stephen, Marcie Jane, Seth Jared and Grace Elise Jones. Their birth weights ranged from 1 pound, 12 ounces to 2 pounds, 11 ounces.
Dr. Gary Burgess says the babies are doing as expected for quintuplets born at 27 weeks. They remain in the neonatal intensive care unit at UT Southwestern's St. Paul University Hospital.
The parents also have an 8-year-old son.