5) Simplify the expression: $(\frac{a-b}{a^2+ab} - \frac{a}{ab+b^2}) : (\frac{b^2}{a^3-ab^2} + \frac{1}{a+b})$

Let's simplify the first part of the expression:

$$\frac{a-b}{a^2+ab} - \frac{a}{ab+b^2} = \frac{a-b}{a(a+b)} - \frac{a}{b(a+b)}$$

Find a common denominator which is $ab(a+b)$:

$$\frac{b(a-b)}{ab(a+b)} - \frac{a^2}{ab(a+b)} = \frac{ab - b^2 - a^2}{ab(a+b)} = -\frac{a^2 - ab + b^2}{ab(a+b)}$$

Now let's simplify the second part of the expression:

$$\frac{b^2}{a^3-ab^2} + \frac{1}{a+b} = \frac{b^2}{a(a^2-b^2)} + \frac{1}{a+b} = \frac{b^2}{a(a-b)(a+b)} + \frac{1}{a+b}$$

Find a common denominator which is $a(a-b)(a+b)$:

$$\frac{b^2}{a(a-b)(a+b)} + \frac{a(a-b)}{a(a-b)(a+b)} = \frac{b^2 + a^2 - ab}{a(a-b)(a+b)}$$

So, the original expression becomes:

$$-\frac{a^2 - ab + b^2}{ab(a+b)} : \frac{a^2 - ab + b^2}{a(a-b)(a+b)} = -\frac{a^2 - ab + b^2}{ab(a+b)} \cdot \frac{a(a-b)(a+b)}{a^2 - ab + b^2} = -\frac{a(a-b)(a+b)}{ab(a+b)} = -\frac{a-b}{b}$$

Final Answer: $-\frac{a-b}{b}$