The attackers were suspected supporters of Christopher "Dudus" Coke, who the government is hunting over a US extradition request.
Elon Parkinson, a presenter on Jamaica's 90 FM radio station, told Al Jazeera: "There is intense gunfire and buildings are being hit by mortar shells. A drone is flying over the area ostensibly identifying targets and as soon as they are identified, soldiers start pelting their houses. So far, five people are said to have been killed and a number of houses have been hit.
"Where it concerns negotiations regarding Mr Coke's surrender - hopes are fading. His loyals indicated to us about an hour ago that any deal between the US and Jamaican authorities would be almost impossible, especially with the way the onslaught is taking place," he said.
Parkison said that 'Coke' has concerns about going into Jamaican custody because his father was supposed to be extradited in 1992.
While being held at a general penitentiary, Coke's father was burnt to death in his prison cell because of what police alleged to be a fire accident.
Streets into the Tivoli Gardens area of West Kingston have been barricaded.
Police have called the barricades, which supporters have used to transform the area into a virtual fortress, an "act of cowardice" and urged Coke to turn himself in.
Tensions in Jamaica rose over the last week after the prime minister reversed his long-standing refusal to extradite Coke to the US on drugs and arms-trafficking charges.
US prosecutors describe Coke as the leader of the "Shower Posse" that murdered hundreds of people by showering them with bullets during the cocaine wars of the 1980s.
Relations between Jamaica and the US grew strained when Jamaica ignored an earlier extradition request for Coke, who is a supporter of the ruling Jamaica Labour party and wields influence in the volatile inner city constituency that Golding represents.