Mysql – GRANT command not working in MySQL Server

Most likely, your user5 has database (i.e. schema) privileges, just not server-wide privileges. So look here.

USE app_db;
SHOW GRANTS FOR user5;

or check in the data dictionary for the same:

SELECT *
FROM INFORMATION_SCHEMA.SCHEMA_PRIVILEGES
WHERE GRANTEE LIKE '%user5%';

if not anything, then maybe also check

SELECT *
FROM INFORMATION_SCHEMA.TABLE_PRIVILEGES
WHERE GRANTEE LIKE '%user5%';

The fundamental problem you have is this:

You cannot grant another user a privilege which you yourself do not have; the GRANT OPTION privilege enables you to assign only those privileges which you yourself possess.

^{— http://dev.mysql.com/doc/refman/5.6/en/grant.html}

This makes sense, since if it were otherwise, then you could just grant privileges to yourself.

There is one way around this, depending on how much flexibility you have with the calling code -- stored procedures can run with the credentials of the defining user (as opposed to the invoking user). If the calling system could call a procedure instead of using GRANT ..., then you can create a procedure that is executable by the restricted user, granting other privileges as appropriate.