May 10: Battle of France begins - German forces invade Low Countries - Battle of the Netherlands begins - Battle of Belgium begins - Invasion of Luxembourg begins - British Invasion of Iceland. - With the resignation of Neville Chamberlain, Winston Churchill becomes Prime Minister of the United Kingdom.
May 13: Winston Churchill, in his first address as Prime Minister, tells the House of Commons of the United Kingdom, "I have nothing to offer you but blood, toil, tears, and sweat." - German armies open a 60-mile (97 km) wide breach in the Maginot Line at Sedan, France.
May 13-May 14: Queen Wilhelmina of the Netherlands and her government are evacuated to London using the British destroyer HMS Hereward.
May 14: Rotterdam is subjected to savage terror bombing by the Luftwaffe; 980 are killed, and 20,000 buildings destroyed. - Recruitment begins in Britain for a home defence force the Local Defence Volunteers, later known as the Home Guard.
May 15: The Dutch army surrenders. - The very first McDonald's restaurant opens in San Bernardino, California. - Women's stockings made of nylon are first placed on sale across the United States. Almost five million pairs are bought on this day.
May 16: President of the United States Franklin D. Roosevelt, addressing a joint session of the U.S. Congress, asks for an extraordinary credit of approximately $900 million to finance construction of at least 50,000 airplanes per year.
May 17: Brussels falls to German forces; the Belgian government flees to Ostend.
May 18: Marshal Philippe Pétain is named vice-premier of France.
May 19: General Maxime Weygand replaces Maurice Gamelin as commander-in-chief of all French forces.
May 20: German forces (2nd Panzer division), under General Rudolf Veiel, reach Noyelles on the English Channel. - The Nazi German concentration and extermination camp Auschwitz-Birkenau, the largest of the German concentration camps, opens in occupied Poland near the town of Os'wie;cim. Between May 1940 and January 1945, around 1.1 million people will be killed here.
May 22: The Parliament of the United Kingdom passes the Emergency Powers (Defence) Act 1940, giving the government full control over all persons and property.
May 24: The Anglo-French Supreme War Council decides to withdraw all forces from Norway.
May 26: The Dunkirk evacuation of the British Expeditionary Force starts. - First free flight of Igor Sikorsky's Vought-Sikorsky VS-300 helicopter.
May 28: King Leopold III of Belgium orders the Belgian forces to cease fighting. Leaders of the Belgian government on French territory declare Leopold deposed. - Winston Churchill warns the House of Commons of the United Kingdom to "prepare itself for hard and heavy tidings."
May 29: The Vought XF4U-1, prototype of the F4U Corsair U.S. fighter later used in WWII, makes its first flight. (source: Wikipedia)