To divide 24 athletes into three equal groups, we need to find a group size that allows for 24 athletes divided by 3 groups.
Calculating the group size:
\[ \text{Group Size} = \frac{24 \text{ athletes}}{3 \text{ groups}} = 8 \text{ athletes per group} \]
However, the requirement states that each group should have no less than 3 athletes and no more than 5 athletes. Given this, we can see that a group size of 8 does not satisfy the conditions, as it exceeds the maximum limit of 5 athletes per group.
Therefore, it is impossible to divide 24 athletes into three equal groups with each group containing between 3 and 5 athletes. The problem does not allow for any possible group sizes under the conditions provided.