Попробуйте следующее:
SET @num := 0, @type := '';
SELECT `year`, `id`, `rate`,
@num := if(@type = `id`, @num + 1, 1) AS `row_number`,
@type := `id` AS `dummy`
FROM (
SELECT *
FROM `h`
WHERE (
`year` BETWEEN '2000' AND '2009'
AND `id` IN (SELECT `rid` FROM `table2`) AS `temp_rid`
)
ORDER BY `id`
) AS `temph`
GROUP BY `year`, `id`, `rate`
HAVING `row_number`<='5'
ORDER BY `id`, `rate DESC;