According toMexican history the 5 de Mayo is about the French-Mexican War in which a poorly supplied and outnumbered Mexican army under General Ignacio Zaragoza defeats a French army attempting to capture Puebla de Los Angeles, a small town in east-central Mexico. Victory at the Battle of Puebla represented a great moral victory for the Mexican government, symbolizing the country's ability to defend its sovereignty against threat by a powerful foreign nation.
In 1861, the liberal Mexican Benito Juarez became president of a country in financial ruin, and he was forced to default on his debts to European governments. In response, France, Britain, and Spain sent naval forces to Veracruz to demand reimbursement. Britain and Spain negotiated with Mexico and withdrew, but France, ruled by Napoleon III, decided to use the opportunity to carve a dependent empire out of Mexican territory. Late in 1861, a well-armed French fleet stormed Veracruz, landing a large French force and driving President Juarez and his government into retreat.
Certain that French victory would come swiftly in Mexico, 6,000 French troops under General Charles Latrille de Lorencez set out to attack Puebla de Los Angeles. From his new headquarters in the north, Juarez rounded up a rag-tag force of loyal men and sent them to Puebla. Led by Texas-born General Zaragoza, the 2,000 Mexicans fortified the town and prepared for the French assault. On the fifth of May, 1862, Lorencez drew his army, well-provisioned and supported by heavy artillery, before the city of Puebla and began their assault from the north. The battle lasted from daybreak to early evening, and when the French finally retreated they had lost nearly 500 soldiers to the fewer than 100 Mexicans killed.
Although not a major strategic victory in the overall war against the French, Zaragoza's victory at Puebla tightened Mexican resistance, and six years later France withdrew. The same year, Austrian Archduke Ferdinand Maximilian, who had been installed as emperor of Mexico by Napoleon in 1864, was captured and executed by Juarez' forces. Puebla de Los Angeles, the site of Zaragoza's historic victory, was renamed Puebla de Zaragoza in honor of the general. Today, Mexicans celebrate the anniversary of the Battle of Puebla as Cinco de Mayo, a national holiday in Mexico.
It is not that mexicans in the United States believe that they are celebrating an independance day, but that they celebrate this day to honorof those who died defending Puebla de Los Angeles, and in doing so, ensure the continuation of the Mexican resistance against the French forces.Here is a small clip I found in youtube:
