Actually, you don't need calculus for this question. You need to be cognizant of this basic fact.

The shortest line between a line ( ) and a point (P) not on the line is the perpendicular line connecting and P.

So what you do is find the equation of the line perpendicular to the given line that goes through the point (-5,4), find where it intersects the original line and then use the length of a line formula.

Sketch the graph so you have a visual idea of what is going on.