On 5 May 1862, a Mexican army defeated French forces at the Battle of Puebla. The French went on to occupy the country and appoint a monarch to rule it in the name of Napoleon III. They were able to get away with that because the U.S. was preoccupied by a Civil War. During the French regime, Mexicans in the United States made the date of the early victory an occasion of patriotic observance. To this day, it's more a Mexican-American holiday than a Mexican one. South of the border, it is not a mandatory holiday, and is only observed intensively in the vicinity of Puebla itself. When "Cinco de Mayo" became a national drinking day in this country, nearly equal to St. Patrick's, I don't really know, but I bet it had more to do with the interests of brewers and bar owners than it did with the ethnic pride of Mexicans.
If you're determined to observe the day, you might want to hoist one for Karl Marx, for whom the defeat of an imperialist army by indigenous forces would probably have been happy news on his 44th birthday. Try not to blame him for all the crap that Lenin and his imitators perpetrated in Marx's name, and why not take a look at the Communist Manifesto and see how much of what he describes, rather than what he predicts, rings true to this day?