As an EU Citizen (and your EU family members), you are automatically a permanent resident after 5 years.
You can apply for a permanent resident card to document this.
Such a card would document the fact that you fulfill the 5 years required for naturalization, should you wish to also become an Irish citizen.
Permanent residence (after 5 years) for ...
Now does it mean that after 5 years of residence in Ireland, I (EU national) and my non-EU family members should apply for PERMANENT RESIDENCE OR IRISH CITIZENSHIP?
It seems to mean that you may each choose one option or the other.
Why would one apply for PR when they can apply for Irish citizenship after 5 years of residence?
One possibility: the current ...