Answer
$$-\cot \left(x\right)$$
Work Step by Step
Simplifying the expression using the sum and difference formulas, we find:
$$\frac{\sin \left(\frac{5\pi }{2}+x\right)}{\cos \left(\frac{5\pi }{2}+x\right)} \\ \frac{\cos \left(\frac{5\pi }{2}\right)\sin \left(x\right)+\cos \left(x\right)\sin \left(\frac{5\pi }{2}\right)}{\cos \left(\frac{5\pi }{2}\right)\cos \left(x\right)-\sin \left(\frac{5\pi }{2}\right)\sin \left(x\right)} \\ \frac{\cos \left(x\right)}{-\sin \left(x\right)} \\ -\cot \left(x\right)$$
