The five are among 18 people, including a woman, on death row for drug offences whose execution will go ahead, according to Sirisena. He did not give a date for the first hanging.
"I am determined to carry out the death penalty for serious drug offenders and I will start with a list (of 18) given to me by the prisons," he told a public meeting in the north of the country.
Sirisena said he would hold talks with talks with Pakistan's new Prime Minister Imran Khan on repatriating the condemned Pakistanis and having them executed there.
Sri Lanka declares state of emergency after Buddhist-Muslim clash
He gave no further details on the feasibility of such a move.
International rights groups and the European Union have asked Sri Lanka to reconsider since Sirisena announced last month that he wanted to end the moratorium on hanging.
Police believe the Indian Ocean island is being used as a transit point by drug traffickers. More than a tonne of cocaine seized in recent years was destroyed by police in January.
Official figures show there were 373 convicts on death row in Sri Lanka, including the 18 drug offenders, as of last month.
Death sentences are still passed for crimes including murder, rape and drug-related offences but the last execution was in 1976.
Nearly 900 people are in prison after being sentenced to death, although many have had their sentences commuted to life or are appealing.
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