#### Answer

$$\frac{1-x}{\left(x-2\right)\left(x+7\right)}$$

#### Work Step by Step

In order to solve the given problem, we first ensure that there are like denominators, meaning that the denominators of each fraction are the same. Then, we combine the numerators, leaving the denominators the same. Finally, we simplify the fraction to get the answer. Doing this, we find:
$$\frac{x^2-5}{\left(x-2\right)\left(x+7\right)}-\frac{\left(x+3\right)\left(x-2\right)}{\left(x+7\right)\left(x-2\right)}\\ \frac{x^2-5-\left(x+3\right)\left(x-2\right)}{\left(x-2\right)\left(x+7\right)}\\ \frac{-x+1}{\left(x-2\right)\left(x+7\right)}$$