Положение модернизатора фиксированного теста неполное

Попробуйте следующее:

SELECT h.year, h.id, h.rate 
FROM (SELECT h.year, h.id, h.rate, IF(@lastid = (@lastid:=h.id), @index:=@index+1, @index:=0) indx 
      FROM (SELECT h.year, h.id, h.rate 
            FROM h
            WHERE h.year BETWEEN 2000 AND 2009 AND id IN (SELECT rid FROM table2)
            GROUP BY id, h.year
            ORDER BY id, rate DESC
            ) h, (SELECT @lastid:='', @index:=0) AS a
    ) h 
WHERE h.indx <= 5;