To simplify the expressions in the given problem, we can use trigonometric identities and properties:

### a) \( A = \cos\left(\frac{\pi}{2} + x\right) + \cos(2\pi - x) + \cos(3\pi + x) \)

- Use the identity:
- \( \cos\left(\frac{\pi}{2} + x\right) = -\sin(x) \)
- \( \cos(2\pi - x) = \cos(x) \)
- \( \cos(3\pi + x) = -\cos(x) \)

Thus,
\[
A = -\sin(x) + \cos(x) - \cos(x) = -\sin(x).
\]

### b) \( B = 2 \cos x - 3 \cos(\pi - x) + 5 \sin\left(\frac{7\pi}{2} - x\right) + \cot\left(\frac{3\pi}{2} - x\right) \)

- Use the identities:
- \( \cos(\pi - x) = -\cos(x) \)
- \( \sin\left(\frac{7\pi}{2} - x\right) = -\sin(x) \)
- \( \cot\left(\frac{3\pi}{2} - x\right) = -\tan(x) \)

Thus,
\[
B = 2 \cos x + 3 \cos x - 5 \sin x - \tan x = 5 \cos x - 5 \sin x - \tan x.
\]

### c) \( C = 2 \sin\left(\frac{\pi}{2} + x\right) + \sin(5\pi - x) + \sin\left(3\pi/2 + x\right) + \cos\left(\frac{\pi}{2} + x\right) \)

- Use the identities:
- \( \sin\left(\frac{\pi}{2} + x\right) = \cos(x) \)
- \( \sin(5\pi - x) = -\sin(x) \)
- \( \sin\left(\frac{3\pi}{2} + x\right) = -\cos(x) \)
- \( \cos\left(\frac{\pi}{2} + x\right) = -\sin(x) \)

Thus,
\[
C = 2 \cos x - \sin x - \cos x - \sin x = \cos x - 2 \sin x.
\]

### d) \( D = \cos(5\pi - x) - \sin\left(\frac{3\pi}{2} + x\right) + \tan\left(\frac{3\pi}{2} - x\right) + \cot(3\pi - x) \)

- Use the identities:
- \( \cos(5\pi - x) = -\cos(x) \)
- \( \sin\left(\frac{3\pi}{2} + x\right) = -\cos(x) \)
- \( \tan\left(\frac{3\pi}{2} - x\right) = -\cot(x) \)
- \( \cot(3\pi - x) = -\cot(x) \)

Thus,
\[
D = -\cos x + \cos x - \cot(x) - \cot(x) = -2 \cot(x).
\]

These are the simplified forms of each expression:
- \( A = -\sin(x) \)
- \( B = 5 \cos x - 5 \sin x - \tan x \)
- \( C = \cos x - 2 \sin x \)
- \( D = -2 \cot(x) \)