Learn English – If we are talking about last night which one is correct to say

You could say either one, though there is some difference between them.

I haven't slept well.

This does not indicate any timeframe. It is possible you did not sleep well for a day, week, month, etc.

I didn't sleep well yesterday.

Here we know it was only one day (yesterday).

The laws of each jurisdiction are different, so without researching I could not say for sure. If this is an important question for you, you must ask someone who works in the Irish government to be specific.

There is also a question of what it means to be "resident". This can be very complicated but usually requires you to live in that place for a significant portion of the year, obtain local documentation (get a license, pay taxes, etc), or own property (and live in it). I don't know what those laws are for Ireland, so you will have to research that as well.

Without further explanation I would assume that it means, going back five calendar years (not including the current year), you had to have been resident for at least three out of those five calendar years. It may include the current year if it is late enough in the year that you can establish "residency" for this year.

Again, this is just a casual reading, and should not be taken as actual advice. Please do the research and ask.