To determine which of the given options is a factor of the polynomial \(15 +7x - 2x^2\), we can use the Factor Theorem. The Factor Theorem states that if a polynomial f(x) has a factor (x - k), then f(k) = 0.

Let's evaluate the polynomial at each of the given values of k to see if any of them are factors:

- For k = -3, f(-3) = 15 + 7(-3) - 2(-3)^2 = 15 - 21 - 18 = -24, so (x + 3) is not a factor.

- For k = 3, f(3) = 15 + 7(3) - 2(3)^2 = 15 + 21 - 18 = 18, so (x - 3) is not a factor.

- For k = 5, f(5) = 15 + 7(5) - 2(5)^2 = 15 + 35 - 50 = 0, so (x - 5) is a factor.

- For k = -5, f(-5) = 15 + 7(-5) - 2(-5)^2 = 15 -35 -50 = -70, so (x + 5) is not a factor.

So, out of the given options, only (x - 5) is a factor of the polynomial \(15 +7x - 2x^2\).