Remove Count In First Line

My query is suppose to capture the student's number, date of birth, and number of students which that students mentors. I am suppose to show only the 5 oldest students

SELECT s.std_num, s.birth_date, COUNT(s2.mentor_num)
From Student s left outer join Student s2
on s2.mentor_num=s.std_num
GROUP BY s.std_num, s.birth_date
ORDER BY s.birth_date ASC;

This function works but the problem is in displaying the five records because whenever I apply the rownum<=5 function the counter returns incorrect results. I tried writing another query to fix it but I could not dispay the counter anymore

SELECT ROWNUM as SENIOR, s.std_num, s.birth_date, COUNT(s2.mentor_num)
FROM (SELECT s1.std_num, s1.birth_date, COUNT
(e2.super_id)
From Student s left outer join Student s2
on s2.mentor_num=s1.std_num
GROUP BY s1.std_num, s1.birth_date
ORDER BY s1.birth_date ASC) S
WHERE row_num<=5;

This code only works if I remove the count in the first line but I need to display the number in my result.