To determine which ordered pair is part of the solution set for the equation \( y = 5x^2 - 2 \), we will substitute the x-value from each ordered pair into the equation and see if the resulting y-value matches.
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For the ordered pair \( (-1, 43) \): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] This does not match 43.
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For the ordered pair \( (-1, 5) \): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] This does not match 5.
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For the ordered pair \( (-1, 3) \): \[ y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] This matches 3.
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For the ordered pair \( (1, 5) \): \[ y = 5(1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \] This does not match 5.
The only ordered pair that is part of the solution set for the equation \( y = 5x^2 - 2 \) is \( (-1, 3) \).