Both choices are wonderful and as said before it boils down to Trapani or Taormina. have you been to Sicily before? wIll you have a car or depend on public transportation. If not renting a car then look at the logistics of bus and train travel to get to where you want to go as it may be the determining factor. There are also private NCC drivers that can be hired for specific daytrips or transfers. You will really not need a car upon arrival in Palermo.. Weather in May should be very pleasant.
Trapani gives you proximity to Segesta, Erice, San Vito lo Capo, Castellammare del Golfo, Scopello, Marsala, Mazara del Vallo, the salt pans and Favignana. All are beautiful choices, and depend upon your interests. With just two nights in Trapani I, personally would prioritize seeing Trapani itself and Erice. The views from the top of the mountain are beautiful. It is often foggy, which creates an eerie atmosphere up there, but the fog and sunshine can shift quickly. If you have a car and are driving from Palermo to Trapani then consider a stop on your way at Castellammare del Golfo or Scopello. Trapani will be less crowded than Taormina but it is also a bigger city. Since you are staying 5 days in Noto area, I suggest staying in Siracusa, particularly Ortigia, over Ragusa. Ortigia and Siracusa have many beautiful sites to see.
Taormina is quite pretty and the teatro greco with Etna in the background is quite a jewel to behold. I also liked the community gardens in Taormina, peaceful, shady, uncrowded and great coastal views. Strolling the streets in Taormina is fun to do. As many have stated, Taormina can get very crowded as it is a prime cruise ship and tourist destination. But if you are keen on going I would go. Be prepared for crowds at the ruins in Agrigento too. If still undecided, look at tourist videos online to help you decide.
Whichever route you choose, I would do it quickly and make your lodging reservations as soon as possible because May is not far off and you will find that many places are already booked. Probably more true of Taormina than Trapani. I would also expect Trapani to be generally cheaper than Taormina.
Enjoy your trip, there are no wrong choices!