Using the strongest language employed to date in the controversy by a senior church figure, Dr Vincent Twomey said the men concerned were causing continuing grave scandal.
The bishops were named in the Commission's report, which investigated the handling of allegations of clerical child sexual abuse in the Dublin Archdiocese.
Dr Twomey said the longer the resignations were delayed, the more damage would be done to the Catholic Church and the victims concerned.
Speaking on the Marian Finucane programme, Dr Twomey said their inaction lacked moral courage.
The five concerned are Doctors Eamonn Walsh and Raymond Field who are still auxiliary Bishops in Dublin and the bishops of Galway and Kildare and Leighlin, Martin Drennan and Jim Moriarty.
Bishop of Limerick Donal Murray of Limerick was also named and he has been in Rome for the past week.
It is believed that he has discussed his future in the hierarchy with the top Vatican officials.
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SIC: RTÉ