Naruto is actually younger than Sasuke and Sakura, but it is stated more than once that the rookie 9 were all born in the same year. Shino is the oldest (born January 23). Sakura is the oldest of team 7 (born March 28).
In Shippuuden, Kushina, Naruto's mom, talks to Sasuke's mom, who is holding baby Sasuke, in the street just days before Naruto's birth.
According to the manga canon, Sasuke's birthday is July 23rd and Naruto's birthday is October 10th.
In Naruto, the standard Academy curriculum is 4 years of classes, and students usually enrol around age 7 or 8 and graduate around age 12. It is not mentioned whether there is some sort of civilian schooling prior to that age.
Genin hopefuls in Naruto could originally enter the Academy as soon as their parents deemed them ready, with some entrants (usually from ninja clans) being as young as 4 or 5, and could choose to take the graduation exam as soon as they had been enrolled a year (like Kakashi, who graduated at age 5).
Since it is not clearly shown/stated it is possible that Naruto enrolled early or that he just took the exams early by his own choice or being pushed by teachers who wanted to get rid of him, as it is also stated in the opening arc that if a student fails the graduation exam 3 times he cannot become a genin.