- May 5 — Siege at Iranian Embassy in London ends as the SAS and police storm the building.
- May 8 — World Health Organization announces smallpox has been eradicated.
- May 13 — Pope John Paul II is shot and critically wounded allegedly by Turkish gunman Mehemet Ali Agca in St Peter's Square, Vatican City.
- May 18 — “An exotic new disease” among homosexuals is reported in New York Native, a gay newspaper. This was the first news story on a disease, which came to be known as HIV/AIDS.
- May 20 — Traci Lords makes her mainstream screen debut at 19 in a leading role of the 1988 remake of Roger Corman’s Not of This Earth (1957).
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