The given inequality is $ x+y < 5$ consider the equation .

$x+y <5$

$(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)

Step 2:

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.

Step 3:

The solution region of the given inequality is the shaded half plane I. not including the line.