judy,
It sounds like you've decided to use the spontaneous approach, so my comments likely won't carry much weight.
I always prefer to pre-book accommodations, especially in busier places like the Cinque Terre. Wandering around an unfamiliar city looking for a place to sleep is wastes valuable touring time, so I prefer to travel as efficiently as possible. That approach also gives me a choice of which area of each city I want to stay, and the price and comfort range I prefer. I always carry directions to each new hotel, so I don't waste any time looking for it when I arrive.
May is spring shoulder season, and I've found that it's often very busy and crowded in some locations. Especially in the C.T., you might consider pre-booking your accommodations, as that will save time and money travelling back and forth to each of the five towns to try and find somewhere to sleep. I know that as I've watched others spend hours trying to find accommodations there.
Happy travels!