To simplify this expression, we first need to deal with the subtraction inside the parentheses:

-4 1/15 - 5/2/3

First, we need to divide the mixed number -4 1/15 by 5/2 (which is the same as division by 5/2):

-4 1/15 ÷ 5/2
To divide mixed numbers, we first convert the mixed numbers to improper fractions:

-61/15 ÷ 5/2
Now, we need to divide fractions by multiplying by the reciprocal of the denominator:

-61/15 * 2/5 = -122/75

Now, we subtract the result from the original expression:

-7 3/5 - (-122/75)

To subtract a negative fraction, we can change it to addition and change the sign of the fraction:

-7 3/5 + 122/75

To add these two fractions, we need to find a common denominator:

-7 45/75 + 122/75

Now we can add the fractions:

-7 167/75

Finally, we can simplify the expression by converting the improper fraction back to a mixed number:

-8 17/75

Therefore, the simplified expression is -8 17/75.