13.2. A third of the sixth-grade students received threes for their math test. How many students received fives if only one student received a two, and fives were received by $\frac{5}{13}$ of the sixth-graders?

$$
(6-7 \text { grade) }
$$
13.2. Students who received threes and fours constitute

$$
\frac{1}{3}+\frac{5}{13}=\frac{28}{39} \text { of the entire class. }
$$

Therefore, the number of students in this class is divisible by 39. Since the class size does not exceed 50 students, there are 39 students in total in the class, with 28 of them receiving threes and fours on the test. Therefore, fives were received by $39-28-1=10$ students.