The problem asks to expand the expression $f(x) = (5x^5 + 5)(-2x^5 - 3)$.

1. Problem Description

The problem asks to expand the expression $f(x) = (5x^5 + 5)(-2x^5 - 3)$.

2. Solution Steps

We use the distributive property (also known as the FOIL method) to expand the product of the two binomials:

$f(x) = (5x^5 + 5)(-2x^5 - 3)$

$f(x) = (5x^5)(-2x^5) + (5x^5)(-3) + (5)(-2x^5) + (5)(-3)$

$f(x) = -10x^{5+5} - 15x^5 - 10x^5 - 15$

$f(x) = -10x^{10} - 25x^5 - 15$

3. Final Answer

The final answer is $f(x) = -10x^{10} - 25x^5 - 15$.