Cinco de Mayo (May 5th) is not the Mexican independence day. Encyclopedia Britannica tells you that Cinco de Mayo is also known as the Anniversary of the Battle of Puebla, and is “a national holiday in Mexico in honor of a military victory in 1862 over the French forces of Napoleon III.”
They continue: “On May 5, 1862, a poorly equipped mestizo and Zapotec force under the command of Gen. Ignacio Zaragoza defeated French troops at the Battle of Puebla, southeast of Mexico City; about 1,000 French troops were killed. Although the fighting continued and the French were not driven out for another five years, the victory at Puebla became a symbol of Mexican resistance to foreign domination.”
And: “The day is celebrated in Mexico, especially in Puebla, with parades and speeches. In some cities there are reenactments of the Battle of Puebla. Cinco de Mayo has also become a festive holiday in parts of the United States with large Mexican American populations, including many cities of the Southwest. Celebrations in the United States often extend beyond the actual day to encompass an entire week, with parades and festivals that include music, dancing, and food.”
Mexico celebrates its independence from Spanish rule on September 16.