5. The function $f(x)$ defined on $\mathbf{R}$. If for any real numbers $x, y$, the equation
$$
f(x-y)=f(x)+f(y)-2xy,
$$
is satisfied, then $f(201)=(\quad)$.
(A) 40400
(B) 40401
(C) 40402
(D) 40403
5. B.

In the given equation, let $x=y$, we get
$$
\begin{array}{l}
f(0)=f(x)+f(x)-2 x^{2} \\
\Rightarrow f(x)=x^{2}+\frac{a}{2}(f(0)=a) .
\end{array}
$$

Taking $x=y=0$, we get
$$
a=2 a \Rightarrow a=0 \text {. }
$$

Upon verification, $f(x)=x^{2}$ satisfies the equation.
Therefore, $f(201)=40401$.