Out of curiosity, is that a hunch or are you aware of any schools teaching multiplication tables even in Kindergarten? This used to be done in second grade when I was a kid.
I'm not aware of any schools teaching multiplication tables in kindergarten, but I did memorize the 9x9 table when I was in kindergarten because my older siblings' Big Kids Notebooks all had the times table on the back and it formed a rhyme/ditty in the local language. After it was explained to me that multiplication was repeated addition, that made perfect sense.
But don't ask me about division, my siblings/parents/whoever tried to explain it as "the opposite of multiplication", which was complete nonsensical gibberish and I didn't learn division until years later.
When I was in kindergarten, I used to do math booklets at home with my mom for fun. I learned basic multiplication sometime around then. 13 years later I majored in engineering.
So I'm not saying it can't be done by any 5 year olds, but it seems young to teach this to the majority of 5 year olds.