About 5,000 patients taking the prescription painkiller methadone die every year from the drug — the vast majority from accidental overdoses — and they account for about 1 in 3 deaths in the United States from prescription opiates, according to a new government report. Many of these deaths could be prevented if doctors curtailed prescribing this drug, said the federal Centers for Disease Control and Prevention in the report released Tuesday. The agency said the number of deaths from methadone overdose had risen sixfold over the past decade but decreased slightly since 2007. That could indicate that more doctors are following US Food and Drug Administration recommendations to prescribe the drug for pain relief only after other opiates fail to work. Methadone is also used to treat heroin addiction, but the CDC report focused only on the4 million methadone prescriptions written annually for pain relief. In Massachusetts, methadone prescriptions account for 9 to 11 percent of prescription painkillers dispensed in the state, according to the CDC report, compared to a national rate of 9 percent. D.K.