The United States is a federal republic and the differences between the laws of the 50 states is greater than people sometimes realize. Education in the United States is VERY decentralized. Not only is it handled by the states, but in most states there is a great deal of local autonomy and control. Everyone tells you something different because everyone you are asking comes from a place where the schools are a little different. It is very common for "elementary school" to mean "kindergarten" and grades 1 through 6, and that means roughly ages 5 through 11. (Age roughly equals grade + 5). The age relationship isn't exact because the rules vary a lot on what age a kid needs to be to start school. The parents of a kid who is almost 6 in September might be given a choice of whether to start him in kindergarten and be one of the oldest kids, or in first grade and be one of the youngest. 6th grade is peculiar too, because sometimes it is included in "elementary school," and sometimes elementary school ends with 5th grade and 6th grade becomes the first year of "middle school." THAT kind of detail can be different between two neighboring towns! (Furthermore, in most states there are both public and private schools. In states with a high Roman Catholic population, many Roman Catholics will send their children to "parochial schools," private elementary schools operated by the Catholic Church).

In the United States there is some variance with age and school, but usually no more than a year. Assuming the plan is for the student to graduate high school when they are 18, they would start 1st grade at around 5-6 years old. There are also somewhat optional schooling that comes before 1st grade known as preschool and kindergarden, so depending on development/maturity some kids may start going to school at 3-4 years old. I started when I was 3 years old and had two years of preschool. I graduated from high school at 17 then turned 18 during that same summer.