Step 1: Recall the concept.
The distance of any point $(x, y)$ from the $y$-axis is given by the absolute value of its $x$-coordinate. That is,
\[
\text{Distance} = |x|
\]
Step 2: Substitute the given coordinates.
For the point $(5, 9)$,
\[
x = 5
\]
\[
\text{Distance from the $y$-axis} = |5| = 5
\]
Step 3: Conclusion.
Hence, the distance of the point $(5, 9)$ from the $y$-axis is $5$ units.