If you're visiting Milan in May, you can check out some of these festivals and events that happen each May in Milan. Note that May 1, Labor Day, is a national holiday, so many businesses, including museums and restaurants, will be closed.
2nd Weekend in May - Pittori del Naviglio Grande. More than 300 artists from around Italy set up an open-air gallery along the south Naviglio Grande for this annual show. Many vendors offer to ship larger works of art, making this event a great place to look for a unique souvenir. More information is available on the Naviglio Grande website.
Early to mid-May - Orticola ai Giardini Pubblici. The Giardini Pubblici, Milan's Public Gardens, are a fantastic place to spend a spring day, especially when the Orticola (plant and flower show) is going on. The technicolor displays of native and exotic plants and flowers will cure any urban angst you may get from touring hectic Milan. More information is available on the Orticola website.
Late May - Cortili Aperti. This event, happening all over Italy, gives visitors a chance to see the courtyards (cortile) and - sometimes - the interiors of private palazzi.
Also the last weekend of May, many wineries are open to visitors with special events for Cantine Aperte.