The equations x² - 4x - 5 = 0 and x² + kx - 15 = 0 share x = 5 as a common root. What is the value of k?

Substitute $x = 5$ into the second equation: $25 + 5k - 15 = 0$, so $5k + 10 = 0$ and $k = -2$, choice D. First confirm that 5 is a root of the first equation: $25 - 20 - 5 = 0$, which is true. Check the answer: $x^2 - 2x - 15 = (x - 5)(x + 3)$, with root 5. Choice A (2) has the wrong sign. Choice B ($-3$) is the other root of the second equation, not $k$. Choice C (3) combines both mistakes. The question asks for the coefficient $k$, not for a root.