Working Permission

Not sure what conditions are on your 5 year  visa but when I had mine it clearly stated I was not to leave HU for longer then 90 days at a time.
You should look over the paperwork sent with your card or check it out with immigration services.
Even now with my 10 permit I can only leave HU legally for one year before reporting it to immigration services.

Your 5 year residence card/visa is for Hungary only. If you move to another EU Country, you have to reapply for a residence visa in that other country after 3 months.

"Your family members may use their residence card to travel to another EU country but if they want to move to another EU country, they have to apply for another residence card in the new host country"

Above from:

https://europa.eu/youreurope/citizens/r … dex_en.htm

And Ireland does not have to give you a new residence or even a new work visa for Ireland. It is up to each country to decide. Your spouse would, else, have to move with you there, and may need to prove to the authorities that your spouse can support you in Ireland if you "loose your job" there. See the above link and its "Sample story" as an example.

You can also ask your potential employer in Ireland to apply for a work visa for you. Then you right to reside in Ireland and work would be on your own merits, not related to your marital status.