1. On May 27, 1539, Spanish conquistador and explorer Francisco Vásquez de Coronado reached the village of Tiguex, near present-day Bernalillo, New Mexico. This marked his arrival in the area he called "New Mexico" and the beginning of his quest to find the fabled Seven Cities of Gold.

2. May 27, 1862, marked the Battle of Peralta, a Civil War engagement fought near the town of Peralta between Union and Confederate forces in New Mexico. The Union troops, led by Colonel Edward R. S. Canby, defeated the Confederate forces under Brigadier General Henry Sibley, who retreated south.

3. On May 27, 1891, the first train arrived in Roswell, New Mexico, as part of the newly constructed El Paso and Northeastern Railroad. This marked a major milestone in the development of Roswell as a transportation hub and helped spur the growth of the town.

4. May 27, 1937, is the date of the first flight of the Hughes H-1 Racer, an aircraft designed and built by aviator Howard Hughes. The plane set a new landplane speed record of 352.39 mph, and the feat helped establish Hughes as a significant figure in aviation history.

5. Finally, May 27, 1967, marked the founding of the American Indian Movement (AIM) in Minneapolis, Minnesota. The organization was founded in response to issues facing Native Americans across the United States, including poverty, discrimination, and loss of land and culture. AIM has since played a significant role in Native American activism and advocacy.