1. Battle of Palo Alto: On May 8, 1846, the US Army and Mexican forces clashed in the first major battle of the Mexican-American War. The battle continued on May 13, with the US Army emerging victorious.

2. First Texas Capitol burned: The original Texas Capitol building in Austin was destroyed by a fire on May 13, 1881. The building was rebuilt, but another fire in 1983 led to its restoration as a museum.

3. First American air victory in WWII: On May 13, 1942, Lt. Edward O'Hare of the US Navy became the first American flying ace of World War II. He shot down five Japanese bombers in a single engagement over the Pacific Ocean.

4. Tornado outbreak: On May 13, 1950, an outbreak of tornadoes swept through Texas, Oklahoma, and Kansas, causing significant damage and loss of life. Over 100 people were killed and thousands were injured.

5. First African American mayor in Texas: On May 13, 1967, Carl Stokes, the first African American mayor elected in a major city in the US, spoke at Texas Southern University in Houston. Stokes served as the mayor of Cleveland, Ohio from 1967 to 1971.