Answer
Please see the graph.
Work Step by Step
Red line: $y\ge x-5$
Blue line: $y\ge -3x+3$
Let's use the point $(0,0)$ to determine what sides of the lines to shade.
Red line: $y\ge x-5$
$y\ge x-5$
$0\ge 0-5$
$0 \ge -5$ (true)
This is true, so we shade the side of the line that does have the point. The inequality has the "greater than or equal to" sign, so we use a solid line.
Blue line: $y\ge -3x+3$
$0\ge -3*0+3$
$0 \ge 0+3$
$0\ge 3$ (false)
This is false, so we shade the side of the line that doesn't have the point. The inequality has the "greater than or equal to" sign, so we use a solid line.
The solution area for the system on inequalities is the area that is shaded both blue and red.