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 $(\quad)$.
(A) $\frac{\sqrt{3}}{3}$
(B) $\frac{2 \sqrt{3}}{3}$
(C) $\frac{4}{3}$
(D) $\sqrt{3}$
5. B.

Given $F(1,0), O(0,0)$.
Let point $M(x, y)$. Clearly, $x \geqslant 0$.
Then $\left(\frac{|M O|}{|M F|}\right)^{2}=\frac{x^{2}+y^{2}}{(x-1)^{2}+y^{2}}$ $=\frac{x^{2}+4 x}{x^{2}+2 x+1}=\frac{4}{3}-3\left(\frac{1}{x+1}-\frac{1}{3}\right)^{2} \leqslant \frac{4}{3}$. When $x=2$, the equality holds.

Therefore, the maximum value of $\frac{|M O|}{|M F|}$ is $\frac{2 \sqrt{3}}{3}$.