Africa

In May, it's late spring in North Africa; the Sahara is by now hot, and is torrid in the vast central and southern areas. Meanwhile, the African monsoon advances towards the north: in the Gulf of Guinea the rains have begun. In the Southern Hemisphere, winter approaches and the temperatures become acceptable in tropical areas, where the rains decrease as well. Further south, in South Africa it begins to be a little cold, and rainfall increases at the lowest latitudes.
Where to go: Algiers, Dakar, Funchal, Gaborone, Harare, Luanda (second half), Lilongwe, Lusaka, Santa Cruz De Tenerife, Tunis

Asia

In May, in the southern part, for example in India, the continent is overheated, waiting for the monsoon, which is already affecting the islands and the southern coasts. On tre other hand, it's spring in temperate and cold areas.
Where to go: Amman, Ankara, Astana (second half), Baku, Beijing, Beirut, Bishkek, Jerusalem, Lhasa, Nicosia (first part), Seoul, Shanghai, Tbilisi (second half), Tokyo, Yerevan

North and Central America

Spring progresses in colder lands; during the month the temperature begins to be pleasant in Canada and Northern United States. In Florida, it's hot and thunderstorms begin. In South-central Mexico, the muggy heat begins to be felt; in Central America by now the rainy season has started.
Where to go: Bermuda, Chicago, Los Angeles, Montréal (second half), New York, San Francisco, Seattle (second half), Toronto (second half), Vancouver (second half), Washington

South America

In the tropical zone, in May there are still widespread rains, but it is autumn in the subtropical zone, where you can take advantage of the milder temperatures. In the Andean region of Bolivia, the dry season begins.
Where to go: La Paz, Rio de Janeiro, Sao Paulo

Europe

In May, temperatures are often mild in Central Europe, and sometimes even in Northern Europe. However, in the first half of the month, sometimes it can still get cold north of the Alps.
Where to go: Amsterdam (second half), Athens, Barcelona, Belgrade, Berlin (second half), Bratislava (second half), Brussels (second half), Bucharest, Budapest (second half), Chisinau, Dublin (second half), Geneva (second half), Istanbul, Kiev (second half), Valletta, Lisbon, London (second half), Luxembourg (second half), Madrid, Milan, Paris (second half), Prague (second half), Podgorica, Rome, Skopje, Sofia, Tirana, Vaduz (second half), Warsaw (second half), Vienna (second half), Zagreb

Oceania

In the Southern Hemisphere, it's the last month of the hot season at tropical latitudes, in which tropical cyclones can still pass; it's autumn in South Australia, and typically the temperatures are still mild, but the rains become a bit more frequent. In the Northern Hemisphere, in Hawaii the rains are quite rare in the sheltered slopes.
Where to go: Honolulu