All five have infection rates higher than 50 cases per 100,000 people over the last two weeks.
Leitrim, which is the smallest county by population, recorded a further 11 infections on Monday. The rise in cases means Leitrim now has a 14-day incidence rate of 49.9, compared with a rate of only 3.1 in neighbouring Sligo.
Up until last Saturday, the county had seen just 90 cases of coronavirus since the pandemic began in Ireland in early March.
Dublin was once again the hardest-hit area in the latest update from the Department of Health, with the capital reporting 56 new infections on Monday night. 182 new cases were confirmed in Dublin on Tuesday.
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Dr Ronan Glynn, the acting chief medical officer, played down the suggestion of a second lockdown in Dublin and Limerick, which has also become an area of concern for the National Public Health Emergency Team.
Dr Glynn warned people from the two counties that the virus is in the community and the next week is crucial.
Speaking at Monday's Covid-19 press briefing, he said talking about another lockdown is "really unhelpful".
"If we have to recommend additional measures, they will be measures to protect people," he said.
"We still have control over this, we still have the power to change the trajectory of this".
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