I thought you meant that May Day (May 1) was the second biggest holiday in Mexico.
I know Cinco de Mayo celebrates the defeat of the French forces at the Battle of Puebla, but I wasn't aware that it was *that* big of a holiday in Mexico (I thought that it was a minor holiday that was exploited by the beer and tequila industries in the U.S.).
You're correct, of course, about the spirits industry's exploitation of 5 May, but the Mexicans (where I was, at least) celebrated loud and long.