Five. (Full marks 20 points) Through the point $M(2,-1)$, draw four chords $P_{i} Q_{i}(i=1,2,3,4)$ of the parabola $y^{2}=x$, and the y-coordinates of points $P_{1}, P_{2}, P_{3}, P_{4}$ form an arithmetic sequence. Find whether: $\frac{P_{1} M}{M Q_{1}}-\frac{P_{2} M}{M Q_{2}}>\frac{P_{3} M}{M Q_{4}}-\frac{P_{4} M}{M Q_{4}}$.
Let $P_{i}\left(y_{i}^{2}, y_{i}\right), Q_{i}\left(y^{\prime 2}, y_{i}^{\prime}\right), \lambda_{i}=\frac{P_{i} M}{M Q_{i}}\left(\lambda_{i} \neq\right.$ $-1), i=1,2,3,4$. By the section formula, we get
$$
\left\{\begin{array}{l}
\frac{y_{i}^{2}+\lambda_{i} y^{\prime 2}}{1+\lambda_{i}}=2, \\
\frac{y_{i}+\lambda_{i} y_{i}^{\prime}}{1+\lambda_{i}}=-1 .
\end{array}\right.
$$

Eliminating $y_{i}^{\prime}$, we get $\left(\lambda_{i}+1\right) y_{i}^{2}+2\left(\lambda_{i}+1\right) y_{i}-\lambda_{i}^{2}+1=0$,
thus
$$
\begin{array}{l}
y_{i}^{2}+2 y_{i}-(\lambda-1)=0 . \\
\therefore \lambda_{i}=\left(y_{i}+1\right)^{2} .
\end{array}
$$
$$
\begin{array}{l}
\therefore\left(\frac{P_{1} M}{M Q_{1}}-\frac{P_{2} M}{M Q_{2}}\right)-\left(\frac{P_{3} M}{M Q_{3}}-\frac{P_{4} M}{M Q_{4}}\right) \\
=\left(\lambda_{1}-\lambda_{2}\right)-\left(\lambda_{3}-\lambda_{4}\right) \\
=\left[\left(y_{1}+1\right)^{2}-\left(y_{2}+1\right)^{2}\right]-\left[\left(y_{3}+1\right)^{2}-\left(y_{4}\right.\right.
\end{array}
$$
$$
\begin{aligned}
& \left.+1)^{2}\right] \\
= & \left(y_{1}-y_{2}\right)\left(y_{4}+y_{2}+2\right)-\left(y_{3}-y_{4}\right)\left(y_{3}+y_{4}+2\right) \\
= & -d\left(y_{1}+y_{2}-y_{3}-y_{4}\right) \\
= & -d(-4 d)=4 d^{2}>0 . \\
& \therefore \frac{P_{1} M}{M Q_{1}}-\frac{P_{2} M}{M Q_{2}}>\frac{P_{3} M}{M Q_{3}}-\frac{P_{4} M}{M Q_{4}} .
\end{aligned}
$$