The function \( f \) is defined as follows. \[ f(x)=\frac{x^{2}+4 x-21}{x^{2}-4} \] Find \( f(-5) \). Simplify your answer as much as possible. If applicable, click on

To find \( f(-5) \), we need to substitute \(-5\) into the function: \[ f(-5) = \frac{(-5)^{2} + 4(-5) - 21}{(-5)^{2} - 4} \] Calculating the numerator: \[ (-5)^{2} = 25, \quad 4(-5) = -20 \] \[ (-5)^{2} + 4(-5) - 21 = 25 - 20 - 21 = 25 - 41 = -16 \] Now calculating the denominator: \[ (-5)^{2} - 4 = 25 - 4 = 21 \] Putting it all together, we have: \[ f(-5) = \frac{-16}{21} \] Thus, the simplified answer is: \[ \boxed{-\frac{16}{21}} \]