This is not the most elegant solution but if you cannot alter the table structure then you can unpivot the data and then apply a user defined variable to get a row number for each student_id. The code will be similar to the following:
select student_id, name, col, data
from
(
SELECT student_id, name, col,
data,
@rn:=case when student_id = @prev then @rn else 0 end +1 rn,
@prev:=student_id
FROM
(
SELECT student_id, name, col,
@rn,
@prev,
CASE s.col
WHEN 'mark1' THEN mark1
WHEN 'mark2' THEN mark2
WHEN 'mark3' THEN mark3
WHEN 'mark4' THEN mark4
WHEN 'mark5' THEN mark5
END AS DATA
FROM marks
CROSS JOIN
(
SELECT 'mark1' AS col UNION ALL
SELECT 'mark2' UNION ALL
SELECT 'mark3' UNION ALL
SELECT 'mark4' UNION ALL
SELECT 'mark5'
) s
cross join (select @rn := 0, @prev:=0) c
) s
order by student_id, data desc
) d
where rn <= 2
order by student_id, data desc;
See SQL Fiddle with Demo. This will return the top 2 marks per student_id
. The inner subquery is performing a similar function as using a UNION ALL to unpivot but you are not querying against the table multiple times to get the result.