Finding a name based on another column count

I have this table employee3_3:

Here John is the manager, that’s why he doesn’t have a managerId value. But to prove he is the manager, I’m asked to write a query to find managers with at least five direct employees.

I tried this:

WITH cte AS
( 
    SELECT 
        name, managerid,
        (SELECT COUNT(b.managerid) 
         FROM employee3_3 AS b) AS result
    FROM
        employee3_3
)
SELECT employee3_3.name
FROM employee3_3
FULL JOIN cte ON employee3_3.name = cte.name
WHERE result = 5    
  AND cte.managerid = NULL

For some reason, it doesn’t return any result.

I also tried this:

WITH cte AS
(
    SELECT  
        managerid, COUNT(managerid) AS number_of_employees
    FROM 
        employee3_3
    GROUP BY
        managerid, managerid
)
SELECT name
FROM employee3_3 AS e
JOIN cte ON e.managerid = cte.managerid
WHERE cte.number_of_employees <= 5

I’m not sure if is my approach that is wrong and I’m not in the right path, or if I’m not using the right functions.

>Solution :

select e.* 
from employee3_3 e
inner join
(select managerId
from employee3_3
group by managerId having count(*) >= 5 
) m on e.Id = m.managerId;

DBFiddle demo

PS: If a manager is meant to be her\his managerId is null then you should add that criteria (then only top level managers would count as manager)