My flight from Boston landed around 7:00 a.m., and I was eating breakfast in downtown Dublin by 9 a.m. You could well have two full days there, which I think is a fair amount of time to see the highlights there. But, as Nancy wrote, if you aren't in until noon, you'll have to work a bit faster to experience as much as possible. You should devote two nights to Dingle, in my opinion. If you only have one night, it will be difficult for you to do the Slea Head drive, go out to some of the pubs for live music at night (doesn't usually start until maybe 9 p.m.), and to see the town. It was our favorite place on our Irish vacation, I can't recommend it enough.
If I were you - and this is just my recommendation, you should do more research to see what interests you most - I would do this: Dublin for two nights, leave early as possible on Friday morning, and drive to Cashel. Stop and see the Rock, maybe walk around the town a bit, then drive to Dingle. This would be a long day of driving, but you would be able to break it up with the stop in Cashel (and any other things that interest you along the way). Spend Friday evening going out to the pubs in Dingle. Saturday morning, do the Slea Head drive, and then you'll have the afternoon and evening to explore Dingle even more. Sunday morning, leave early and drive to the Cliffs of Moher (be sure to take the ferry from Tarbert to Killimer, it'll save you some time). After the Cliffs of Moher, settle in for Sunday night at a village somewhere between the Cliffs and Shannon (or alternatively, stay in Galway for the night). Both Galway and the Cliffs of Moher are about 1.5 hours from the Shannon airport.
That is two days with a fair amount of driving (from Dublin to Dingle via Cashel, and then Dingle to the Cliffs of Moher). It is pretty ambitious, but you'll be able to squeeze in a lot into your 5 days, and see some of the lovely scenery along your drives.
