HMMT 2004 E3

Suppose $f$ is a function that assigns to each real number $x$ a value $f(x)$, and suppose the equation

$$f\left(x_{1}+x_{2}+x_{3}+x_{4}+x_{5}\right)=f\left(x_{1}\right)+f\left(x_{2}\right)+f\left(x_{3}\right)+f\left(x_{4}\right)+f\left(x_{5}\right)-8$$

holds for all real numbers $x_{1}, x_{2}, x_{3}, x_{4}, x_{5}$. What is $f(0)$ ?