Answer
$$\frac{x+4}{2\left(x-5\right)}$$
Work Step by Step
Using the rules of exponents and cancelling common factors in the numerator and the denominator, we find:
$$\frac{\left(x+5\right)\times \:2\left(x^2-16\right)}{\left(4x-16\right)\left(x^2-25\right)}\\ \frac{\left(x+5\right)\left(x^2-16\right)}{2\left(x-4\right)\left(x^2-25\right)}\\ \frac{\left(x+5\right)\left(x+4\right)\left(x-4\right)}{2\left(x-4\right)\left(x+5\right)\left(x-5\right)}\\ \frac{x+4}{2\left(x-5\right)}$$
