5 days in Ireland Where would you go 1st time around?

It would help to know what airport you are flying into.

Hard to limit it to 5 days but I guess it depends on whether you want to see the city or the country.
Here are my suggestions for 5 days:
If you like city and museum things:
Dublin for history, museums, great hop on hop off
bus, and a good starting place for bus day trips.
we especially liked the one day tour to

Glendalough and Wicklow mountains.
Gallway is a great college city with lots to do
and see and more modern than Dublin. I was glad I
saw the Aran Islands but would not go there
again. There were just so many other places I
enjoyed more.
I have not yet been to Cork (my next trip) and will
spend an entire week in Northern Ireland when I
next go to Ireland.
If you like the country and nature:

Dingle Peninsula is by far my favorite from my
trip in 2006. We spent 2 days there and could
have stayed longer. Some of the best trad music
from our trip was there down by the harbor.
Connemara day trip from Galway is also quite pretty
and is a good one day bus tour.
If you go in the summer you might do better to do some more out of the way things which are just as beautiful and avoid things like the Ring of Kerry and Cliffs of Moher and other "popular tourist" spots. I hear the crowds can be quite bad.
If you have any questions feel free to email me.
Have a GREAT trip!

Ooops....sorry I forgot one place...We loved the Rock of Cashel and the surrounding area. Great place to explore and views of countryside not to be believed. We stayed at a B&B at the foot of the Rock called Rockside run by Joan and Ren (great fun) and the view at night of the Rock is wonderful.
I would go back there again.

I think Dale had great suggestions. Dingle is my favorite place in Ireland, so I would do at least two nights there, possibly three. Then I would head up the west coast to see the Burren and Cliffs of Moher and maybe do a day trip to the Aran Islands..

Or you could head over to Kinsale, seeing the Ring of Kerry on the way.