How do you write an equation in standard form for a line passing through (5, –2) and is parallel to x = 4?

The line $x = 4$ has infinite slope as will any line parallel to it. So our target line cannot be expressed in point slope form or slope intercept form.
$x = 5$
since it passes through a point $\left(5 , - 2\right)$,
which has $x$ coordinate $5$.