SASMO 2014 Primary 6 (Grade 6) Contest Question 11

The digits 3, 4, 5, 6 and 7 are all used to write a five-digit number $ABCDE$, where $ABC$ is divisible by 4, $BCD$ is divisible by 5 and $CDE$ is divisible by 3. Find all possible values of $ABCDE$.