The express train was traveling to the southern city of Chennai Sunday night when it ran into the herd crossing railroad tracks near Ganjam district, the authorities said.
A tusker, three females and a calf died, the Times of India reported. One of the female elephants also was in an advanced stage of pregnancy.
A local forest official said the animals that were killed, along with 20 other elephants, had recently migrated from a sanctuary and had been seen roaming in the area after splitting into groups.
There was fog in the area at the time of the accident, officials said. The carcasses of the elephants were removed.
State Forest Minister Bijayshree Routray expressed shock over the incident, saying railway authorities had been warned by forest officials that the elephant herds would cross the tracks at night, the Times reported. He said state officials also had erected fluorescent "elephant crossing zone" signs across a stretch of several miles.
"Despite all this, such a tragedy took place," Routray was quoted as saying.