1. The Battle of Cieneguilla: On September 5, 1854, a clash between a group of U.S. soldiers and a band of Apache warriors took place near Cieneguilla, New Mexico. Despite being outnumbered, the Apache successfully repelled the U.S. force, causing a significant setback for the military's efforts to subdue the Apache in the region.

2. The founding of Las Cruces: On September 5, 1849, the town of Las Cruces was officially established in the Mesilla Valley. The area had been inhabited for centuries by indigenous peoples and was part of Mexico until the end of the Mexican-American War.

3. The discovery of gold in Hillsboro: On September 5, 1877, prospectors discovered rich veins of gold in the mining town of Hillsboro in southwestern New Mexico. The discovery sparked a rush of miners and settlers to the area, and Hillsboro became one of the most prosperous towns in the region.

4. The establishment of the New Mexico State Fair: The first New Mexico State Fair was held on September 5, 1938, in Albuquerque. The fair has since become an annual tradition, showcasing the best of agriculture, livestock, and culture in the state.

5. The opening of the Sandia Peak Tramway: On September 5, 1966, the Sandia Peak Tramway officially opened in Albuquerque. The tramway, one of the longest in the world, offers stunning views of the city and the surrounding Sandia Mountains.