- May 1 Catcher Moses Walker is acknowledged as the first African-American to play major league baseball joining the Toledo Blue Stockings
- May 1 Construction begins on Chicago's 1st skyscraper (10 stories)
- May 1 Proclamation of the demand for eight-hour workday in the United States.
- May 13 Institute for Electrical & Electronics Engineers (IEEE) forms in New York
- May 14 Anti-Monopoly party forms in US
- May 16 10th Kentucky Derby: Isaac Murphy aboard Buchanan wins in 2:40.25
- May 16 Italian inventor Angelo Moriondo receives patent for 1st espresso machine
- May 17 Alaska becomes a US territory
- May 19 Ringling Brothers circus premieres in Baraboo, Wisconsin
- May 22 1-armed pitcher Hugh Daily fanned 13 hitters
- May 23 12th Preakness: S Fisher aboard Knight of Ellerslie wins in 2:39.5
- May 24 Anti-Monopoly party & Greenback Party forms People's Party in US
- May 26 Australian cricket fast bowler Fred Spofforth takes 7-34 & 7-3 against an England XI in a tour match in Birmingham; match over in just 4 hours
- May 29 Europe's first steam cable trams start in Highgate, London
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