5. For a line segment $A B$ of fixed length 3, whose endpoints move on the parabola $y^{2}=x$, the midpoint of segment $A B$ is $M$. Try to find the shortest distance from point $M$ to the $y$-axis.
(Let the distances from points $A, B, M$ to the directrix be $d_{1}$, $d_{2}$, $d_{0}$ respectively. Then $d_{0}=\frac{d_{1}+d_{2}}{2}=\frac{|A F|+|B F|}{2} \geqslant \frac{|A B|}{2}=\frac{3}{2}$. The equality holds when $A B$ passes through point $F$, at which time the distance from $M$ to the $y$-axis is minimized, with the minimum value being $\frac{5}{4}$.)