To solve the given mathematical expression, follow these steps:

\[ \left( \frac{2}{15} - \frac{1}{3} \right) - 3 \cdot \frac{1}{2} + \left( \frac{-3}{5} \right)^5 \div \left( \frac{-3}{5} \right)^3 \]

1. Simplify the fraction subtraction inside the parentheses:
\[ \frac{2}{15} - \frac{1}{3} \]
Convert \(\frac{1}{3}\) to have a common denominator with \(\frac{2}{15}\):
\[ \frac{1}{3} = \frac{5}{15} \]
\[ \frac{2}{15} - \frac{5}{15} = \frac{2 - 5}{15} = \frac{-3}{15} = \frac{-1}{5} \]

2. Simplify the multiplication:
\[ 3 \cdot \frac{1}{2} = \frac{3}{2} \]

3. Simplify the division of the powers:
\[ \left( \frac{-3}{5} \right)^5 \div \left( \frac{-3}{5} \right)^3 \]
Using the property of exponents \(\left( \frac{a}{b} \right)^m \div \left( \frac{a}{b} \right)^n = \left( \frac{a}{b} \right)^{m-n}\):
\[ \left( \frac{-3}{5} \right)^5 \div \left( \frac{-3}{5} \right)^3 = \left( \frac{-3}{5} \right)^{5-3} = \left( \frac{-3}{5} \right)^2 = \frac{9}{25} \]

4. Combine all the simplified parts:
\[ \frac{-1}{5} - \frac{3}{2} + \frac{9}{25} \]

5. Convert all fractions to a common denominator to combine them:
The common denominator for 5, 2, and 25 is 50.

\[ \frac{-1}{5} = \frac{-10}{50} \]
\[ \frac{3}{2} = \frac{75}{50} \]
\[ \frac{9}{25} = \frac{18}{50} \]

6. Combine the fractions:
\[ \frac{-10}{50} - \frac{75}{50} + \frac{18}{50} = \frac{-10 - 75 + 18}{50} = \frac{-67}{50} \]

So, the final result is:
\[ \frac{-67}{50} \]