calculus - Understanding Cauchy Mean Value Theorem

I got a hard time to understand the Theorem from Cauchy Mean Value Theorem. Could someone please to help me explain this?

Let I be an open interval and $n$ be a natural number and suppose that the function $f: I \rightarrow R$ has n derivatives. Suppose also that the point $x_0$ in $I$:

$f^{(k)}(x_0) = 0$ for $0 \le k \le n-1$

Then, for each point $x \not = x_0$ in $I$, there is a point $z$ strictly between $x$ and $x_0$ at which

$f(x) = \frac{f^{(n)}(z)}{n!}(x-x_0)^n$

Then my homework is giving $f(x) = (x-2)^5$ with $f(x_0) = f'(x_0) = ... = f^{n-1}(x_0)$ with $x_0 = 2$ and $n=3$, find all possible $z$ to satisfy the Theorem above.