In American English, including the "and" in this context can be either very formal, or informal.
In spoken American English, this "and" is natural. In informal speech, it is often shortened to "'n'". When speech is written down, most contractions like "'n'" are either spelled out in full (like "and") or omitted entirely.
American primary school teachers tell children to not say "and" in this context. Most American primary school teachers teach both English and arithmetic. I think they want the children to be clear about whether they are stating a math problem, like "two and three make five", or whether they are naming a number, like "one hundred twenty-five". Thus, using "and" in this context is informal in American English.
On the other hand, there are famous American examples of formal speeches that use "and" in similar contexts. For example, Abraham Lincoln's Gettysburg address includes the phrase "four score and seven years ago". Thus, very formal texts sometimes use "and" in this context.
For normal writing in American English, I recommend omitting the "and" in this context.