From the set {(-2, -5), (0, 10), (5, 8), (8, -3)}, which ordered pairs are a part of the solution set for 5x + 5y > 45?

Let's go through each of the given points and plug in the coordinates

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Plug in (x,y) = (-2,-5)

5x + 5y > 45
5(-2) + 5(-5) > 45 ... replace x with -2; replace y with -5
-10 - 25 > 45
-35 > 45

The last inequality is false, so (-2,-5) is not in the solution set.

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Plug in (x,y) = (0, 10)

5x + 5y > 45
5*0 + 5*10 > 45
0 + 50 > 45
50 > 45

The last inequality is true so (0,10) is in the solution set
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Plug in (x,y) = (5,8)

5x + 5y > 45
5*5 + 5*8 > 45
25+40 > 45
65 > 45

The last inequality is true so (5,8) is in the solution set
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Plug in (x,y) = (8,-3)

5x + 5y > 45
5*8 + 5*(-3) > 45
40 - 15 > 45
25 > 45

The last inequality is false, so (8,-3) is not in the solution set
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Summary: The points (0, 10) and (5,8) are in the solution set

Check out the attached image to see a visual representation of this. 
Notice how point B and point C are in the red shaded region.