Hundreds of troops joined fire fighters in the rescue operation after the 300-foot garbage dump crashed following a fire in Kolonnawa, a suburb north of here.
A 12-year-old boy and two teenaged girls died at the hospital while three other people who were pulled from the wreckage of homes were already dead by the time they arrived at the hospital, officials said.
Around 50 to 100 houses were completely destroyed, said attorney Nuwan Bopage.
The military has been deployed to rescue people who might be trapped, police said, adding that the army and an air force helicopter were also pressed into service to douse the flames.
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Police said the true scale of the damage remained unclear.
"A search for survivors is under way," the police said in a statement.
Sri Lanka's parliament was recently warned that 23 million tonnes of garbage at Kolonnawa dump was a serious health hazard.
The local residents had protested about the environmental damage as a result of the open dump where some 800 tonnes of solid waste is added daily.
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