Nope. That’s September 16. Cinco de Mayo is both simpler and more complicated, being at root a commemoration of a Mexican peasant army’s 1862 defeat of an invading contingent of the French Foreign Legion. Nowadays, it’s more of a family celebration among Mexican-Americans, with only a look-back at the old country, where it’s hardly observed at all.
One of the best explanations of the history of it that I’ve seen is by Austinite Don Miles. His 296-page non-fiction Indie book, Cinco de Mayo: What Is Everyone Celebrating, is a fascinating adventure story involving a pathetic Austrian royalist and his nervous wife, poorly-armed Mexican revolutionaries, some die-hard Confederates, Unconditional Surrender Grant, and much more. You really should get the book. (A used copy goes for just $2.84 plus S&H) Too bad it’s not an e-book. At least, if it is, I can’t find a copy.
THE TEXAS SCRIBBLER 
See, I always thought Cinco De Mayo was a holiday created by Dos Equis and Corona.
You learn something new every day.
Heh. Might as well be. Also by Taco Bell, though I don’t think many Mexicans patronize them.