DELETE FROM t1, t2, t3, t4, t5 
USING table1 AS t1 
LEFT JOIN table2 AS t2 ON t1.inst_id=t2.inst_id 
LEFT JOIN table3 AS t3 ON t2.inst_id=t3.inst_id 
LEFT JOIN table4 AS t4 ON t3.inst_id=t4.inst_id 
LEFT JOIN table5 AS t5 ON t4.inst_id=t5.inst_id 
WHERE t1.inst_id = 2

DELETE t1, t2 FROM t1 INNER JOIN t2 INNER JOIN t3
WHERE t1.id=t2.id AND t2.id=t3.id;

Or: 
DELETE FROM t1, t2 USING t1 INNER JOIN t2 INNER JOIN t3
WHERE t1.id=t2.id AND t2.id=t3.id;