y < x - 5

First we draw the graph of the boundary line y = x - 5.
Two points on that line are (0,-5) and (3,2).  We must draw the line
dotted because the inequality is < and therefore does not include 
the boundary line:



Since the line does not go through the origin we can use (0,0) as
a test point to see whether the origin is a solution.  If it is a
solution then all points are on the same side of the boundary line 
as the origin and if the origin is not a solution, all the solutions
are on the side the origin is not on.  So we substitute (x,y) = (0,0)
in the original inequality:

y < x - 5
0 < ·0 - 5
0 < -5

That is false so we must shade the side of the line that the origin
is not on:



Edwin