I would definitely try to get out into the countryside. Dublin is great and all, but I don't think there's enough to see there to fill 5-7 days. The Burren, Cliffs of Moher, and Ring of Kerry are all really neat things to do. (But, for the Ring of Kerry, you'll need to rent a car and be able to devote probably about three days of your trip to it. I think the other two are day trips from Dublin.)
Good luck!