Generate correct data in select tag

Question

Structure of the table category:

id | parent_id | name
----------------------
1  | NULL      | test1
2  | NULL      | test2
3  | 1         | test3
4  | 1         | test4
5  | 3         | test5
6  | 2         | test6
7  | 6         | test7
8  | 3         | test8

It is tree.

So, this is what I want in PHP: I have id (it can be function argument), for example 5 and I want generate select tags, (in this example 3 level) so I want generate something like this: https://jsfiddle.net/Lh8y2mzh/

test6 and test7 are not in select and this is what I want. It should work recursively I think. Any help? How to make the function?