Tente esta consulta -
DELETE f
FROM table1 AS f
JOIN table2 AS dsy
ON dsy.f1 = f.f1
JOIN table3 AS ds
ON ds.f2 = f.f2
JOIN table4 AS dp
ON dp.f3 = f.f3
JOIN table5 AS dg
ON dg.f4 = f.f4
WHERE
dsy.school_year = 2011 AND ds.id = 29620 AND dp.id = 14120 AND dg.grade_level = 5;