Welcome to Michele's Forum!    

There is no simple answer to your question.  A lot depends on where, when and how you plan to travel.  Generally speaking, in May, you should always be able to find a place to spend the night -- However:

1 May 2017 is the Monday holiday the Irish celebrate as their Labor Day, but it is early enough in the month that it shouldn't affect you.  Still, if there is any sort of Festival or other event happening in the town you are planning to stay, availability MAY be rather scarce.

Another consideration is that even though there may be availability SOMEWHERE in the vicinity, finding a place 'Close-In' (That provides 'Walking Distance' access to pubs, eateries and attractions) could be booked up -- as they tend to be the most popular.

Tourist Information Offices will book you into accommodations for a very small fee (2  or 3 Euro) anywhere in the Republic, but not all towns have them and they may not all be open, in May.  Spending an hour or so chasing down a place to stay can be rather wasteful (and stressful!), as well.

Likewise, many B&B operators often form unofficial 'networks' and are often good sources of recommendations for stays in other towns, assuming that you have a rough idea in the morning of where you expect to end up that evening.

I often leave two or three 'Blanks' in my schedule -- even on visits in June and July -- but I wouldn't feel terribly comfortable doing my entire trip 'On The Fly' . . .

Also, you should DEFINITELY pre-book any nights planned for Dublin -- and I would strongly recommend that you always pre-book your First and Last night's lodgings, no matter which Airport you are flying into, or out of.