May is the fifth month of the Human year.
On May 5th, 2151, the crew of Enterprise made First Contact with the Axanar. (ENT: "Fight or Flight")
Enterprise's spatial torpedoes were calibrated in the heat of battle in May of 2151 after an early launch in April of the same year. (ENT: "Silent Enemy")
Kaitaama ascended to the throne of Krios Prime as First Monarch on May 16th, 2153. (ENT: "Precious Cargo")
Duras resumed pursuit of the Enterprise NX into the Delphic Expanse in May of 2153, after waiting for Enterprise to complete a refit on Earth. (ENT: "The Expanse")
Kathryn Janeway was born on May 20th. (VOY: "Year of Hell")
Enterprise was attacked in the Borderland by two Orion interceptors on May 17th, 2154. (ENT: "Borderland")
The Augment Crisis took place in May of 2154. (ENT: "Borderland", "The Augments")
Doctor Arik Soong returned to Cold Station 12 in May of 2154 to retrieve Augment embryos stored there. (ENT: "Cold Station 12")
Many events in the non-canon novel Articles of the Federation took place in May of 2380.