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Verified answer
F(x) = x² + 2x - 5 = (x + 1)² - 6(fog)(x) = x² - 4x - 2
(g(x) + 1)² - 6 = x² - 4x - 2
(g(x) + 1)² = x² - 4x + 4
(g(x) + 1)² = (x - 2)²
g(x) + 1 = x - 2
g(x) = x - 3
g(-5) = -5 - 3 = -8