1985-May

• May 4 – The 30th Eurovision Song Contest takes place in Gothenburg, Sweden.
• May 5 – U.S. President Ronald Reagan joins German Chancellor Helmut Kohl for a controversial funeral service at a cemetery in Bitburg, Germany, which includes the graves of 59 elite S.S. troops from World War II.
• May 11
  • The FBI brings charges against the suspected heads of the 5 Mafia families in New York City.
  • Fire engulfs a wooden stand in the Valley Parade stadium in Bradford, England during a football match, killing 56.
• May 13 – Philadelphia, Pennsylvania Mayor Wilson Goode orders police to storm the radical group MOVE's headquarters to end a stand-off. The police drop an explosive device into the headquarters, killing 11 MOVE members and destroying the homes of 61 city residents in the resulting fire.
• May 15 – An explosive device sent by the Unabomber injures John Hauser at UC Berkeley.
• May 19 – John Anthony WalkerJr., is arrested by the FBI for passing classified Naval communications on to the Soviets.
• May 23 – Thomas Patrick Cavanaugh is sentenced to life in prison for attempting to sell stealth bomber secrets to the Soviet Union.
• May 25 – Bangladesh is hit by a tropical cyclone and storm surge, which kills approximately 10,000 people.
• May 29 – Heysel Disaster: 38 spectators are killed in rioting on the terraces during the European Cup final between Liverpool F.C. and Juventus at Heysel Stadium in Brussels, Belgium.
• May 31 – Forty-one tornadoes hit in Ohio, Pennsylvania, New York and Ontario, killing 76.