Read the question carefully. To solve this problem, you must know the definition of a solution.
Identify the bottom line. Make a note: k = ?
Assess your options. You could plug in answer choices, but it may take a lot of time to eliminate incorrect answers. Instead, think about how you can use the information that you were given. What variable are you normally solving for in these equations? An x! The problem tells you that one of the solutions is -5. That means that x can equal -5. Once you plug in x = -5, it will be easy to solve for k.
Attack the problem.
(-5)2 + k(-5) + 15 = 0
25 - 5k + 15 = 0
-5k = -40
k = 8
Loop back. You solved for k, which is your bottom line. Look down at your answer choices.
The correct answer is (E).
This is a medium level question.