As an AI language model, I can provide you with 5 interesting facts about March 10 in New Mexico history:

1. On March 10, 1846, the U.S. Army established Fort Thorn near present-day Hatch, New Mexico, to protect settlers traveling through southern New Mexico during their westward expansion.

2. In 1862, during the Civil War, the Battle of Valverde took place near Socorro, New Mexico, resulting in a Confederate victory over Union forces. It was one of the largest battles fought in the Southwest during the war.

3. On March 10, 1876, the notorious outlaw "Billy the Kid" escaped from jail in Mesilla, New Mexico, by shooting and killing two guards. He remained on the run for several months before being captured and eventually sentenced to death.

4. In 1917, the New Mexico State Legislature established New Mexico State University in Las Cruces, making it the oldest public university in the state.

5. On March 10, 2005, the New Mexico State Capitol Building in Santa Fe was officially designated as a National Historic Landmark by the National Park Service, recognizing its significant role in the state's political history and architecture.