The given inequality is $ x+y < 5$ consider the equation .
$(5,0) $ and $(0,5)$ satisfy the equation
The line $x+y =5$ is represented as a dotted line in the graph.
The line divides the plane into two half planes I and II.
Select a point not an line say (0,0)
We observe that , $0+0 <5$
$ 0 < 5$
Which is true (0,0) satisfies the given inequality
$\therefore $ half plane II is not the solution region.
The solution region of the given inequality is the shaded half plane I. not including the line.