Many, mistakenly, think, that the 5th of May is the day of the Mexican Independence. This is however not the case. The Independence of Mexico was declared on 16th September 1810.
The bank holiday of 5th of May is celebrated in memory of the victory of a rather ramshackle Mexican army over nearly twice as strong and much better armed French troops in the battle of Puebla in 1862, 52 years later. The background is as follows:
During the 1850s, Mexico suffered a serious economic crisis which lead to the accumulation of huge foreign loans and debts. To obtain some relief and try to get the crisis under control, President Benito Juarez issued a moratoruim on 17th July 1861, declaring that all foreign debts would be suspended for two years and payment would resume thereafter.
The answer to that measure from Spain, Great Britain and France was to invade the country and practically raid her in order to obtain payment by whatever means they could. Whereas Spain and the UK quickly settled, the French refused to leave. Under Napoleon III, they fully intended to annex Mexcio and establish an emperor in the person of the Habsburg Prince Maximillian, whom they had already brought along for the purpose.
Brave Mexicans, mostly Chicanos, Mestizos and Zapotec Indians under General Ignacio Zaragoza, badly armed and vastly outnumbered by the well trained French Army, nevertheless managed to shatter and defeat the French.
Since then, 5th of May is celebrated in Mexico in honour of the spirit of independence and bravery of the Mexican people.