(5) Let the focus of the parabola $y^{2}=4 x$ be $F$, the vertex be $O$, and $M$ be a moving point on the parabola, then the maximum value of $\frac{|M O|}{|M F|}$ is ( ).
(A) $\frac{\sqrt{3}}{3}$
(B) $\frac{2 \sqrt{3}}{3}$
(C) $\frac{4}{3}$
(D) $\sqrt{3}$
5 B Hint: From the conditions, we know $F(1,0)$, $O(0,0)$, and the coordinates of point $M$ are $(x, y)$. Clearly, $x \geqslant 0$, then
$$
\begin{aligned}
\left(\frac{|M O|}{|M F|}\right)^{2} & =\frac{x^{2}+y^{2}}{(x-1)^{2}+y^{2}}=\frac{x^{2}+4 x}{x^{2}+2 x+1} \\
& =\frac{4}{3}-3\left(\frac{1}{x+1}-\frac{1}{3}\right)^{2} \leqslant \frac{4}{3} .
\end{aligned}
$$

When $x=2$, the equality holds, hence the maximum value of $\frac{|M O|}{|M F|}$ is $\frac{2 \sqrt{3}}{3}$.