Ok, here goes the awful truth: ... 5 de mayo is NOT our most important celebration, nor our national day. In fact, it is only celebrated in one place of the whole country (and I bet not many know why).
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I really don't know why it became so important for the Mexicans that live in the US, and I have to admit that also I don't know much about the historical background of that day.
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I do know that on may 5th 1862, a battle took place in the city of Puebla, Mexico. The very strong and experienced French army was beaten by the not so preparated Mexicans. That is why it is kind of important.
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Nowadays, in Puebla they have a military parade and everyone has the day off (nice, but just in Puebla).
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Well, that is everything I know about it, if anyone wants to add something else, I will appreciate it.
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By the way, the most important national party in Mexico takes place on September 16th, when we celebrate our independence day.