- May 1 91st Kentucky Derby: Bill Shoemaker wins aboard Lucky Debonair, the third of his 4 Derby victories
- May 1 Stanley Cup: Montreal Canadiens beat Chicago Blackhawks 4-0 in Game 7 to take title 4-3
- May 1 USSR launches Luna 5; later impacts on Moon
- May 1 Battle of Dong-Yin, a naval conflict between ROC and PRC, takes place.
- May 2 "New Faces of 1965" opens at Booth Theater NYC for 52 performances
- May 2 Early Bird satellite goes into commercial service
- May 3 1st use of satellite TV, Today Show on Early Bird Satellite
- May 3 3rd Mayor's Trophy Game, Mets beat Yanks 2-1 in 10
- May 3 Cambodia drops diplomatic relations with the US
- May 3 Don Steele, begins a 40+ year radio career at KRTH (Los Angeles California)
- May 3 KTCI TV channel 17 in St. Paul-Minneapolis, MN (PBS) 1st broadcast
- May 3 Pulitzer prize awarded to Irwin Unger (Greenback Era)
Baseball Record
May 4 Willie Mays 512th HR breaks Mel Ott's 511th NL record
Willie Mays
- May 5 First large-scale US Army ground units arrive in South Vietnam
- May 6 Lawry & Simpson complete opening stand of 382 against W Indies
- May 7 WAOW TV channel 9 in Wausau, WI (ABC) begins broadcasting
- May 8 1st shut put over 70' (Randy Matson 70' 7")
- May 9 The Beatles attend a Bob Dylan concert
- May 9 Luna 5 launched (USSR) 1st attempt to soft land on Moon (fails)
- May 11 "Flora, the Red Menace" opens at Alvin Theater NYC for 87 performances
- May 11 1st of 2 cyclones in less than a month kills 35,000 (India)
- May 11 Bangladesh windstorm kills 17,000
- May 11 Ellis Island added to Statue of Liberty National monument
- May 11 USSR performs nuclear test at Eastern Kazakh/Semipalitinsk USSR
- May 11 West Indies becomes 1st holders of the Frank Worrell Cricket Trophy
- May 12 Israel & West Germany exchange letters beginning diplomatic relations
- May 13 Rolling Stones record "Satisfaction"
- May 13 Several Arab nations break ties with West Germany after it established diplomatic relations with Israel
- May 14 2nd Chinese atom bomb explodes
- May 14 US performs nuclear test at Nevada Test Site
- May 15 90th Preakness: Ron Turcotte aboard Tom Rolfe wins in 1:56.2
- May 15 Canadian Football Players Association organizes
- May 15 Igor Vodic beats Mad Dog Vachon in Omaha, to become NWA champ
- May 16 "Roar of the Greasepaint" opens at Shubert Theater NYC for 232 performances
- May 16 Balt Oriole Jim Palmer's pitching debut, beats Yankees 7-5 & homers
- May 16 Bomb destroys USAF base Bien Hoa, South Vietnam
- May 16 WNJU TV channel 47 in NY-Linden, NY (TEL) begins broadcasting
- May 16 The Campbell Soup Company introduces SpaghettiOs under its Franco-American brand
- May 16 18th Cannes Film Festival: "The Knack...and How to Get It" directed by Richard Lester wins the Grand Prix du Festival International du Film
- May 18 Gene Roddenberry suggests 16 names for Star Trek Captain; they include Kirk
- May 18 WTAF TV channel 29 in Philadelphia, PA (IND) begins broadcasting
- May 19 Patricia R Harris named 1st US black female ambassador (Luxembourg)
- May 19 West Ham United of England win 5th European Cup Winner's Cup against 1860 München of West Germany 2-0 in London
- May 20 Pakistani Boeing 720-B crashes at Cairo Egypt, killing 121
- May 20 Yorkshire all out for 23 v Hampshire at Middlesbrough
- May 22 "Super-cali-fragil-istic-expi-ali-docious" hits #66
- May 22 Beatles' "Ticket to Ride" single goes #1
- May 22 Mad Dog Vachon beats Igor Vodic in Omaha, to become NWA champ
- May 23 Franz Jonas elected President of Austria
- May 23 Pontoon ferry overturned on Shire River, Malawi, kills 150
- May 24 Supreme Court declares federal law allowing post office to intercept communist propaganda is unconstitutional
- May 25 Dave Davies of The Kinks stumbles and is knocked unconscious on stage
- May 25 India and Pakistan border fights
Boxing Title Fight
May 25 Muhammad Ali KOs Sonny Liston in 1 for heavyweight boxing title rematch
Muhammad Ali
Sonny Liston
- May 25 Roel van Duyn, Martijn Ananar & Rob Faado align in Provo
- May 26 Dutch Voting Rights Bill passes
- May 26 Revised International Convention on Safety of Life at Sea takes effect
- May 27 10th European Cup: Internazionale beats Benfica 1-0 at Milan
- May 28 Fire & explosion at Dhori mine in Dhanbad India kills 400
- May 29 Phillies Dick Allen hits 529' HR out of Connie Mack Stadium
Tennis Open
May 29 French Men's Tennis Championships: Fred Stolle beats fellow Australian Tony Roche 3-6, 6-0, 6-2, 6-3 for his first Grand Slam singles title
Tony Roche
- May 29 64th Women's French Championships: Lesley Turner Bowrey beats Margaret Smith (6-3, 6-4)
- May 30 France performs nuclear test at Ecker Algeria (Underground)
- May 30 Viet Cong offensive against US base Da Nang, begins
- May 30 Vivian Malone is 1st black to graduate from University of Alabama
- May 31 Jim Clark becomes 1st foreigner in 49 years to win Indianapolis 500 - 3:19:05.370 (242.506 km/h)
- May 31 12th National Film Awards (India): "Charulata" wins the Golden Lotus