Simplify the expression $$\frac{x^5y - xy^5}{5(3y - x)} \cdot \frac{2(x - 3y)}{x^4 - y^4}}$$ for $$x = -\frac{1}{7}$$ and $$y = -14$$.

Step 1: Factor the expression.

$$\frac{xy(x^4 - y^4)}{5(3y - x)} \cdot \frac{2(x - 3y)}{(x^2 - y^2)(x^2 + y^2)}$$

Step 2: Simplify by canceling terms.

Note that $$(x - 3y) = -(3y - x)$$ and $$(x^4 - y^4) = (x^2 - y^2)(x^2 + y^2)$$.

$$\frac{xy}{5} \cdot \frac{-2}{(x^2 - y^2)(x^2 + y^2)}$$

Step 3: Substitute the given values of x and y.

$$x = -\frac{1}{7}$$, $$y = -14$$.

$$x^2 = \frac{1}{49}$$, $$y^2 = 196$$.

$$x^2 - y^2 = \frac{1}{49} - 196 = \frac{1 - 196 \cdot 49}{49} = \frac{1 - 9604}{49} = -\frac{9603}{49}$$.

$$x^2 + y^2 = \frac{1}{49} + 196 = \frac{1 + 196 \cdot 49}{49} = \frac{1 + 9604}{49} = \frac{9605}{49}$$.

Step 4: Calculate the final value.

$$\frac{(-\frac{1}{7})(-14)}{5} \cdot \frac{-2}{(-\frac{9603}{49})(\frac{9605}{49})} = \frac{2}{5} \cdot \frac{-2 \cdot 49^2}{-9603 \cdot 9605} = \frac{2}{5} \cdot \frac{-2 \cdot 2401}{-(9603 \cdot 9605)} = \frac{2}{5} \cdot \frac{4802}{92200015} = \frac{9604}{461000075}$$.