1988: May

May 4 - PEPCON disaster in Henderson, Nevada: A major explosion at an industrial solid-fuel rocket plant causes damage extending up to 10 miles away, including Las Vegas's McCarran International Airport.
May 14 - Bus collision near Carrollton, Kentucky: A drunk driver going the wrong way on Interstate 71, hits a converted school bus carrying a church youth group from Radcliff, Kentucky. The resulting fire kills 27, making it tied for 1st in the U.S. for most fatalities involving 2 vehicles to the present day. Coincidentally, the other 2-vehicle accident involving a bus that also killed 27 occurred in Prestonsburg, KY 30 years prior.
May 14 - Wimbledon wins the English FA Cup after beating Liverpool 1–0 at Wembley. The southwest Londoners had pulled off one of the greatest upsets in the history of English football, as they had been top division members for just 2 years and had joined the Football League only 11 years earlier. Liverpool, meanwhile, had won a total of 30 major trophies including 17 league titles.
May 15 - Soviet war in Afghanistan: After more than eight years of fighting, the Red Army begins withdrawing from Afghanistan.
May 16 - A report by U.S. Surgeon General C. Everett Koop states that the addictive properties of nicotine are similar to those of heroin and cocaine.
May 16 - California v. Greenwood: The U.S. Supreme Court rules that police officers do not need a search warrant to search through discarded garbage.
May 24 - Section 28 (outlawing promotion of homosexuality in schools) is passed as law by Parliament in the United Kingdom.
May 31 - U.S. President Ronald Reagan addresses 600 Moscow State University students, during his visit to the Soviet Union.