There are lots of families with children at Easter, lots of young people during the month of spring break, and then starting around the end of May/beginning of June you have all the families vacationing. The first couple of weeks in May are slower - with great rates! In my experience it does tend to be a period with less families and more adults and I've cruised in March, April & May.
Good choice. I also am considering a cruise in May - probably the Destiny.