* Astronomy

The First Council of Nicaea convened in Bithynia in AD 325. 
http://en.wikipedia.org/wiki/First_Council_of_Nicea

Research of AIDS was first published in 1983
http://en.wikipedia.org/wiki/HIV#Discovery

In 526 during late May, probably between the 20th and the 29th, a major earthquake hit Syria and Antioch 
http://astronomy.activeboard.com/t42940092/526-antioch-earthquake/

The 1883 eruption of Krakatoa began in May 1883 and culminated with its destruction on 27 August 1883.
http://en.wikipedia.org/wiki/1883_eruption_of_Krakatoa

Operation Redwing was a United States series of 17 nuclear test detonations from May to July 1956.
http://astronomy.activeboard.com/t42940150/cherokee-operation-redwing-nuclear-test/

The Battle of Dun Nechtain was fought between the Picts and the Northumbrians on 20 May 685.
http://astronomy.activeboard.com/t42940046/the-battle-of-dun-nechtain/

The massacre in the Main Temple of the Aztec capital Tenochtitlan occurred on May 20, 1520.
http://en.wikipedia.org/wiki/The_massacre_in_the_Main_Temple

Vasco da Gama landed in Calicut on 20 May 1498
https://en.wikipedia.org/wiki/Vasco_da_Gama

Pioneer Venus 1 or Pioneer Venus Orbiter was launched on May 20, 1978
http://en.wikipedia.org/wiki/Pioneer_Venus_project

The first flight if SpaceShipOne was on May 20, 2003
http://en.wikipedia.org/wiki/SpaceShipOne#Flights

The NOAA-18 weather forecasting satellite was launched on May 20, 2005,
http://en.wikipedia.org/wiki/NOAA-18

Hayato, known before launch as K-Sat, is a Japanese satellite which was launched in May 2010
http://en.wikipedia.org/wiki/Hayato_(satellite)

Negai ("Wish") is a Japanese satellite which launched in May 2010.
http://en.wikipedia.org/wiki/Negai_(satellite)

Akatsuki, formerly known as the Venus Climate Orbiter, was launched on 20 May 2010.
http://astronomy.activeboard.com/t16977373/venus-climate-orbiter/

The spacecraft IKAROS was launched on 20 May, 2010
http://wiki.solarsails.info/index.php/IKAROS

Spoiler

Launch of the Proton-M/Breeze-M rocket carrying the Telstar 14R commsat, 2011
http://www.youtube.com/watch?v=TCMa4GHj7X8

GSAT-8 was launched on May 21, 2011 from Kourou, French Guiana. 
http://en.wikipedia.org/wiki/GSAT-8

X-37B/OTV-4 was launched on the 20th May 2015
http://astronomy.activeboard.com/t60229469/x-37botv-4/

At the age of 34, on the morning of May 20, 1932, Amelia Earhart set off from Harbour Grace, Newfoundland
http://en.wikipedia.org/wiki/Amelia_Earhart#1932_transatlantic_solo_flight

Spoiler

On 20 May 1784, the Marchioness and Countess of Montalembert, the Countess of Podenas and a Miss de Lagarde flew aboard on a tethered balloon in Paris

World Metrology Day celebrates the signature of 17 nations of The Metre Convention on 20 May 1875
http://en.wikipedia.org/wiki/World_Metrology_Day

'The Last Days on Mars' is a 2013 science fiction-horror film directed by Ruairí Robinson
https://en.wikipedia.org/wiki/The_Last_Days_on_Mars

On 20 May 1964 the first measurement by the Dicke radiometer showed the presence of the microwave background
http://en.wikipedia.org/wiki/Cosmic_microwave_background#History

On May 20th, 1910, Halley's Comet came within 0.15 AU of the Earth
http://cometography.com/pcomets/001p.html

Asteroid (293) Brasilia was discovered by French astronomer Auguste Charlois on May 20, 1890 in Nice
http://en.wikipedia.org/wiki/293_Brasilia

Asteroid (510) Mabella was discovered by American astronomer Raymond Smith Dugan on May 20, 1903 in Heidelberg
http://en.wikipedia.org/wiki/510_Mabella

The daylight Zeta Perseids meteor shower
http://astronomy.activeboard.com/t42945757/daytime-zeta-perseids-meteor-shower/