May 1 – At 4:00 a.m., John George Kemeny and Thomas Eugene Kurtz run the first computer program written in BASIC (Beginners' All-purpose Symbolic Instruction Code), an easy to learn high level programming language which they have created. BASIC is eventually included on many computers and even some games consoles.

May 2 - An explosion caused by Viet Cong commandos causes carrier USNS Card to sink in the port of Saigon. Some 400–1,000 students march through Times Square, New York, and another 700 in San Francisco, in the first major student demonstration against the Vietnam War. Smaller marches also occur in Boston, Seattle, and Madison, WI.

Henry Hezekiah Dee and Charles Eddie Moore, hitchhiking in Meadville, Mississippi, are kidnapped, beaten and murdered by members of the Ku Klux Klan. Their badly decomposed bodies are found by chance in July during the search for missing activists Chaney, Goodman, and Schwerner.

May 7 - Pacific Air Lines Flight 773 crashes near San Ramon, California, killing all 44 aboard; the FBI later reports that a cockpit recorder tape indicates that the pilot and co-pilot had been shot by a suicidal passenger.

At a mail rockets demonstration by Gerhard Zucker on Hasselkopf Mountain near Braunlage (Lower Saxonia, Germany), three people are killed by a rocket explosion.

May 9 – South Korean President Park Chung Hee reshuffles his Cabinet, after a series of student demonstrations against his efforts to restore diplomatic and trade relations with Japan.

May 12 – Twelve young men in New York City publicly burn their draft cards to protest against the Vietnam War, the first such act of war resistance.

May 23 – Madeline Dassault, 63, wife of a French plane manufacturer and politician, is kidnapped while leaving her car in front of her Paris home; she is found unharmed the next day in a farmhouse 27 miles (43 km) from Paris.

May 24 – The crowd at a football match in Lima, Peru, riots over a referee's decision in the Peru-Argentina game; 319 are killed, 500 injured.

May 27 – The ongoing Colombian conflict starts, with an assault by 1,000 Colombian soldiers, backed by fighter planes and helicopters, against about 50 guerrillas in the community of Marquetalia.

May 28 – The Charter of the Palestine Liberation Organization (PLO) is released by the Arab League.

May 29 – Having deposed them in a January coup, South Vietnamese leader Nguyen Khanh has rival Generals Tran Van Don and Le Van Kim convicted of "lax morality". (source: Wikipedia)