Giving a detailed description about events leading to the firing in Velachery area in the city, she said a police team had reached the spot on information that the robbers were holed up in a house and asked them to come out.
"Police told the robbers in Tamil and Hindi to come out of the house, but the latter not only declined to do so, but also opened fire," she said.
Jayalalithaa, intervening during a discussion on home grants, said police had retaliated with a view to protect themselves and public (as it was a residential area) and added that the five were delcared brought dead to a hospital.
Two Inspectors were also injured in the incident, she said, adding members of the force were not trigger happy to open indiscrimnate fire.
Among the weapons found in possession of the deceased were pistols, shotgun and a revolver and cash, she said.
Jayalalithaa said these persons were wanted in connection with cases in other states, where they had even allegedly used explosive devices as part of their criminal activities.