Typically it is between 5 and 10 but there is no official age requirement. Most gyms prefer gymnasts to be between 7 and 9 when beginning Level 3 gymnastics as this will give them the proper amount of time to prepare before moving on to Level 4.
Level 3 gymnasts can be anywhere from 5 to 10 years old or even older if they start the sport late. Of course the earlier you start the better so that you learn the basic fundementals.