This query gives me an error in MySQL 5.1.57, works in 5.1.53 though:
DELETE f
FROM table1 AS f
JOIN table2 AS dsy
JOIN table3 AS ds
JOIN ta
Have you tried removing all of your table alias? There is a similar solution proposed here. So the following might work:
DELETE table1
FROM table1
JOIN table2
JOIN table3
JOIN table4
JOIN table5
WHERE
table2.f1 = table1 .f1
AND table3.f2 = table1.f2
AND table4.f3 = table1.f3
AND table5.f4 = table1.f4
AND table2.school_year = 2011
AND table3.id = 29620
AND table4.id = 14120
AND table5.grade_level = 5;