The Burren (outside of Galway) is where you'll find the wildflowers (in season).
Plenty of green hills all over Western Ireland. You seem to have limited time, so I don't know that you can fit in both the Galway area and Dingle in just 5 days (does that include travel days, or are you in area for 5 full days?) without it being a blur. Pick one.
Galway makes an excellent base for day tours if you are not planning on renting a car and driving yourself. From Galway you can get tours for the Burren, Aran Islands, Connemara, Cliffs of Mohrer, Ailwee Caves and others. Galway also offers a lot in the way of great restaurants, pubs and nightlife (including a lot of live music, dance and theater productions).
Dingle is best seen with a car.