1. On July 13, 1945, the first atomic bomb test (Trinity Test) was conducted at Alamogordo, New Mexico. The test was a part of the Manhattan Project, a research project that produced the first nuclear weapons during World War II.

2. The Taos Pueblo, a Native American community in northern New Mexico, celebrates the feast day of Saint Bonaventure on July 13. The festivities include traditional dances and ceremonies, and visitors can witness the community's customs and traditions.

3. July 13 is designated as New Mexico Statehood Day, which marks the day when New Mexico was admitted to the Union as the 47th state in 1912. The statehood proclamation was signed by President William Howard Taft.

4. In 1881, Sheriff Pat Garrett shot and killed infamous outlaw Billy the Kid in Fort Sumner, New Mexico. The incident happened on July 13 and remains a significant event in the history of the Wild West.

5. On July 13, 1868, the Battle of Washita River took place in the Oklahoma Territory, which was then a part of New Mexico. The battle was a part of the Indian Wars and pitted the United States Army against the Cheyenne tribe. The battle resulted in a significant victory for the US Army and marked the beginning of the end for the Cheyenne defense of their lands.