Let's analyze each statement about the function \( y = f(x) = 2\sin x - \sqrt{3} \).

### A. \( f\left(\frac{5\pi}{2} - x\right) = 2\sin x - \sqrt{3} \)

To check this, we need to calculate \( f\left(\frac{5\pi}{2} - x\right) \):

\[
f\left(\frac{5\pi}{2} - x\right) = 2\sin\left(\frac{5\pi}{2} - x\right) - \sqrt{3}
\]
Using the sine subtraction formula, we have:
\[
\sin\left(\frac{5\pi}{2} - x\right) = \cos x
\]
Thus,
\[
f\left(\frac{5\pi}{2} - x\right) = 2\cos x - \sqrt{3}
\]
This does not equal \( 2\sin x - \sqrt{3} \) except for specific values of \( x \). Therefore, statement **A** is **false**.

### B. Hàm số \( y = f(x) \) là hàm chẵn (Even function)

A function \( f(x) \) is even if \( f(-x) = f(x) \). Checking this:
\[
f(-x) = 2\sin(-x) - \sqrt{3} = -2\sin x - \sqrt{3}
\]
This is not equal to \( f(x) \). Hence, statement **B** is **false**.

### C. Trong đoạn \( \left[ 0; \frac{5\pi}{2} \right] \) phương trình \( f\left(\frac{5\pi}{2} - x\right) = 0 \) có 4 nghiệm.

We solve:
\[
2\cos x - \sqrt{3} = 0 \implies \cos x = \frac{\sqrt{3}}{2}
\]
The solutions to this in the interval \( \left[ 0; \frac{5\pi}{2} \right] \) are:
\[
x = \frac{\pi}{6}, \quad x = \frac{11\pi}{6}
\]
These two solutions correspond to the cosine function in the range of \( 0 \) to \( 2\pi \) and will repeat for \( 0 \) to \( \frac{5\pi}{2} \):

Considering \( \frac{5\pi}{2} \) exceeds \( 2\pi \), the full behavior of the cosine function will give two additional solutions in that extra \( \left(2\pi, \frac{5\pi}{2}\right) \) range.

Thus, statement **C** is **true**.

### D. Trong đoạn \( \left[ 0; \frac{5\pi}{2} \right] \) phương trình \( f\left(\frac{5\pi}{2} - x\right) = 0 \) có nghiệm lớn nhất bằng \( \frac{13\pi}{6} \).

From the previous findings, the range of \( x \) solutions was \( \frac{\pi}{6}, \frac{11\pi}{6}, \) and the second cycle gives one more solution around \( \frac{13\pi}{6} \), but it does not lie in our range since it exceeds \(\frac{5\pi}{2} = \frac{15\pi}{6}\). Thus the maximum valid solution comes before this.

Therefore, statement **D** is **false**.

### Summary of Statements:

- **A:** False
- **B:** False
- **C:** True
- **D:** False