Hello Kayla,
Graph the first inequality y > -x - 2. Since, it has > than symbol use dashed line. Now, your graph is divided in two parts. For the easiest way to find out which side of the graph you need to shade pick origin(0, 0) as your checking point. Substitute x = 0 and y = 0 in y > -x - 2. You'll get
0 > 0 - 2
0 > -2 which is true. So, that means shade the side of the graph which has the origin.
Repeat the same method for the second inequality y < -5x + 2. You'll get the overlapped region as an answer.
If you've any difficulty myself or any other tutor will help you. Good luck.