Hi Annie,
The first time we went to Madeira, the best thing we did was drive up above the clouds to Pico do Arriero, where the air was so clear and the clouds below looked like cotton wool. Unfortunately we did it again the second time we went but we never came out of the top of the clouds - very disappointing!
Nun's Valley (Curral das Freiras) has some spectacular scenery, and from Cabo Girao there are fabulous views along the coast.
Take a sled ride from Monte down to the town of Funchal. Two men pull you down with ropes in a wicker sled on wooden runners, and it's really exciting

the way they seem to miss the cars!!
May will be a lovely time to go, beautiful weather and lots of flowers. Have a great time!