No, there's no evidence of this, and quite a bit to militate against the notion.

First, the positive evidence. The encyclopedic work compiled by Friar Sahagún and many Nahua scribes from interviews conducted in the decades post-Conquest, The General History of the Things of New Spain speaks directly to this. This is what it has to say about children born during this time:

And if one were then born, there was great fear of it, there was ignoring of it. And if it were a man, they named him Nemon, Nentlacatl, Nenquizqui.^1 Nowhere was he counted, nowhere did he belong. He was a profitless man. And if it were a woman, she was a profitless woman.

There's nothing about infanticide, and the Historia is not a text that shies away from discussing such matters. Durán, writing later, simply says that children born during this time period were "considered unfortunate."^2 Again, nothing about mass infanticide over a 5 day period.

There's a tendency to exoticize American cultures, particularly in such a way to depicts them as less rational than stoutly post-Enlightenment Europeans. I should know, because while I was undergoing a vision quest my spirit animal appeared and told me that my great-great-great-great-grandmother (who was a Cherokee princess) told me I should live in harmony with The Land, which cannot be owned. In Mesoamerica, simply invoking the "Ancient Mayans" is usually enough to set a thousand crystals vibrating with source energy.^*

The Aztecs, by dint of their penchant for human sacrifice and their well publicized kerfuffle with Cortés et al., have a different sort of twist on this othering. Not only are they depicted as irrational and superstitious, but they are envisioned as doing so in a self-defeating way. They cringe at shadows and stab themselves in the foot, literally, and are thus shown to be almost childish in comparison to hard-nosed, logical Europeans who have put aside childish things.

The truth of the matter is that while their were superstitions about birthdays in Mesoamerica, though these mostly were centered on the trecenas of the tonalpohualli, the 260 day calendar.^3 A child born during the Tochtli trecena, for example, was thought to be lucky, but with a tendency towards being a useless drunk. Those born in the period starting with 1 Acatl were thought to often be liars, while those born in the trecena of Quetzpalin were assumed to be brave. People born on Friday the 13th were considered to be unlucky, while those born on July 4th were considered exceptionally patriotic, and those born under the sign of Scorpio were good in the sack... wait, I think I've made some sort of comparison to prove a point.

So why even have these "unlucky/lucky" days? Not something I feel qualified to answer (though maybe a subject /u/itsallfolklore might have a few words on). The point is to show that ascribing certain attributes to people based on their birthdates shades towards the ubiquitous. And yet, somehow, people born during certain trecenas or under certain astrological signs (or who are Iron Roosters, or born on a certain saint's day, or are Enneagram Type 6, INTJs, etc.) manage to get on with living their lives.

Really though, to think that these superstitions would so override the minds of the people in Mesoamerica to the point of mass murder of babies born during certain period is absurd to the point of insulting. This is particularly the case when you consider the way Nahuas viewed their children. A new baby was seen as a gift, referred to as jewels or quetzal plumes, and to bear a child was considered a woman's highest honor in life. Having a designated 5 day period wherein all those precious jewels were sacrificed simply doesn't make sense outside of sixth grade humbug.

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^(1 These are riffs on the theme of useless, futile, good for nothing, etc. Regardless, it was common practice to name children after the day they were born.)

^(2 Book of Gods and Rites and the Ancient Calendar)

^(3 From Aguilar-Moreno, Handbook to Life in the Aztec World)

^(* Edit: This tidbit seems to be causing an undue amount of distraction. It is a humorous riff on the fact that othering of Native Americans often results in them being a receptacle for supernatural, irrational, and outright fallacious beliefs, something which is relevant to the question. Please align your chakras accordingly.)