Last year my son's kindergarten was doing combinatorics problems nearly identical to the combinatorics problems my cousin was teaching to math and computer science majors at the University of Pennsylvania.
The Ivy League college students were expected to use more sophisticated strategies to arrive at more precise and complete solutions than the kindergarteners (who were effectively brute-forcing the answers), but the questions were essentially the same.
I talked a bit with the kindergarten teacher about it. She had never heard the term "combinatorics" and was a little surprised to hear that the same problems were being taught at such a high level. In her class the point wasn't to get the "right" answer, but for the kids to spend time thinking about the relationships of the numbers, and from my conversations with my son I think it succeeded.
When folks read about kids doing algebra or calculus at age 5 they think back to their high school algebra and calculus courses and assume that kids are learning about slope intercepts, quadratic equations, derivatives and integrals. But just as my son's kindergarten class never heard the word "combinatorics" yet used combinatorics problems to learn more about how numbers work together, there are many ways for very young kids to learn concepts that are core to algebra and calculus without having to memorize formulas or visualize the X and Y axes. And spending time thinking about those concepts can help them tremendously later in life.
Heck, I was doing geometry at age 5 when I had to learn about angles to make the Apple Logo turtle draw cool pictures on the computer screen. I don't think I realized it was "geometry" until I got to middle school, but that doesn't mean it wasn't helpful to my ultimate ability to understand math.