Answer
Please see the graph.
Work Step by Step
Red line: $x+3y\le7$
Purple line: $y\le5$
Black line: $x\ge0$
Orange line: $y\ge0$
To determine what sides of the lines to shade, we use a point not on the line. We can use (1,1) for the lines.
Red line:
$x+3y\le7$
$1+3*1\le7$
$1+3\le7$
$4\le7$ (true, so we shade the left side of the line)
Purple line:
$y\le5$
$1\le5$ (true, so we shade under the line)
Black line:
$x\ge0$
$1\ge0$ (true, so we shade the right side of the line)
Orange line:
$y\ge0$
$1\ge0$ (true, so we shade above the line)
The solution area is the overlap of the four inequalities. The boundary area is bounded by the points $(0,0)$, $(7,0)$, and $(0, 2.33)$.