Similar to April, May is at the early start of the summer season and therefore visitors can often get great deals on accommodation and tours. This time of year is also great for glacier exploration and mountaineering.
Spring is in the air, and the capital city of Reykjavik is starting to fill with more visitors as the summer tourist season starts to pick up. Overall a great time to visit, plenty of daylight to explore the country and most roads in the countryside/highlands are opening up after the winter. Great time to visit the north and drive through the Eastfjords of Iceland where fewer tourists will be this time of year.