Hello, andyboy179!
$\displaystyle \text}I need to shade this region: }\;\begin{Bmatrix} y \:<\: 3x1 \\ y \:<\: 3 \\ x \:<\: 5 \end{Bmatrix}$
You have shaded the wrong side of each inequality.
Graph the lines: .$\displaystyle \begin{Bmatrix}y \:=\:3x1 \\ y \:=\:3 \\ x \:=\:5 \end{Bmatrix}$
Then shade the region below or to the left of the lines.
Code:

 /
 *
 /
 / 
3 / 
  *  /  +  
 /:::::
 /:::::
/::::::
*::::*
/:::::::5
/::::::::
/:::::::::

The final region is the area that has been shaded three times.