Consider the following for the two (02) items that follow: A...

Given the functional equation $f(xy) = f(x+y)$ for all real values of $x$ and $y$.

Substituting $y = 0$ into the given equation:

$f(x \cdot 0) = f(x + 0)$

$f(0) = f(x)$

This shows that $f(x)$ is a constant function, meaning it takes the same value for all real $x$.

We are given that $f(5) = 10$.

Since $f(x) = f(0)$ for all $x$, substituting $x = 5$ gives:

$f(5) = f(0)$

Therefore, $f(0) = 10$.

Answer: $10$