The Verdict: Not eligible
Residence in Northern Ireland does not count towards ordinary naturalisation. If you are married to an Irish citizen, look at the marriage route, which counts the whole island; otherwise check descent.
The ordinary test counts residence in the State, which means the Republic only. Years in Belfast or Derry do not count, however lawful, and the Common Travel Area makes no difference to it.
The spouse or civil partner of an Irish citizen is the exception: that route counts residence anywhere on the island, so you may already qualify on the years you have.
And if you were born in Northern Ireland before 2005, or have a parent or grandparent born anywhere on the island, you may be entitled to Irish citizenship already and need not naturalise at all.