MySQL Equivalent Query or JOIN query
If you don 't try to understand the meaning of the request and simply adapt it to MySQL then:

UPDATE userrole ur
LEFT JOIN ( SELECT b.id 
            FROM userrole a 
            INNER JOIN userrole b ON a.roleid = b.roleid 
                                 AND a.region = b.region
            WHERE a.userid = 6 
              AND b.userid = 5 ) sq ON ur.id = sq.id
SET ur.userid = 6 
WHERE ur.userid = 5
WHERE sq.id IS NULL



If you try to understand the task then it looks like (it seems) "alter userid from 5 to 6 if the record with the same (roleid,region) and userid=6 not exists yet". If so the task may be solved by:

UPDATE userrole t1
LEFT JOIN userrole t2 ON (t1.roleid, t1.region) = (t2.roleid, t2.region)
                     AND t2.userid = 6
SET t1.userid = 6
WHERE t1.useris = 5
  AND t2.userid IS NULL