Sure! Here is how you can solve these problems:

1) Tìm x biết:
- (a) \( (x - 1)^{-3} = \frac{1}{8} \)

**Solution:**
\[
(x - 1)^{-3} = \frac{1}{8} \implies (x - 1)^3 = 8 \implies x - 1 = 2 \implies x = 3
\]

- (b) \( (x + 5)^{\frac{2}{3}} = \frac{64}{125} \)

**Solution:**
\[
(x + 5)^{\frac{2}{3}} = \left(\frac{4}{5}\right)^2 \implies x + 5 = \left(\frac{4}{5}\right)^3 \implies x + 5 = \frac{64}{125} \implies x = -5 + \frac{64}{125}
\]

- (c) \( (2x - 1)^3 = \frac{8}{27} \)

**Solution:**
\[
(2x - 1)^3 = \left(\frac{2}{3}\right)^3 \implies 2x - 1 = \frac{2}{3} \implies 2x = \frac{5}{3} \implies x = \frac{5}{6}
\]

2) Tìm x biết:
- (a) \( (3 - x)^{-2} = -\frac{27}{64} \)

No real solution (as \((-3)^2\) is positive).

- (b) \( (x - 5)^{\frac{3}{2}} = \frac{1}{-27} \)

Invalid since \(\frac{1}{-27}\) as root is not defined properly; complex solution needed.

- (c) \( (6 - x)^3 = -\frac{125}{8} \)

**Solution:**
\[
(6 - x)^3 = \left(-\frac{5}{2}\right)^3 \implies 6 - x = -\frac{5}{2} \implies x = 6 + \frac{5}{2}
\]

3) Tìm x biết:
- (a) \( \left( x - \frac{1}{3} \right)^{-3} = -\frac{8}{27} \)

No real solution as cube of \(-\frac{2}{3}\) is not defined in \(\mathbb{R}\).

- (b) \( \left( x - \frac{1}{2} \right)^3 = \frac{27}{8} \)

**Solution:**
\[
\left( x - \frac{1}{2} \right)^3 = \left(\frac{3}{2}\right)^3 \implies x - \frac{1}{2} = \frac{3}{2} \implies x = 2
\]

- (c) \( \left( x - \frac{1}{2} \right)^3 = -8 \)

**Solution:**
\[
\left( x - \frac{1}{2} \right)^3 = (-2)^3 \implies x - \frac{1}{2} = -2 \implies x = -\frac{3}{2}
\]

4) Tìm x biết:
- (a) \( \left( x - \frac{1}{3} \right)^{-3} = \frac{8}{27} \)

**Solution:**
\[
\left( x - \frac{1}{3} \right)^{-3} = \left(\frac{2}{3}\right)^3 \implies x - \frac{1}{3} = \frac{3}{2} \implies x = \frac{3}{2} + \frac{1}{3}
\]

- (b) \( \left( x - \frac{1}{8} \right)^3 = -\frac{8}{125} \)

**Solution:**
\[
\left( x - \frac{1}{8} \right)^3 = \left(-\frac{2}{5}\right)^3 \implies x - \frac{1}{8} = -\frac{2}{5} \implies x = -\frac{2}{5} + \frac{1}{8}
\]

- (c) \( \left( x - \frac{5}{2} \right)^3 = -\frac{1}{8} \)

**Solution:**
\[
\left( x - \frac{5}{2} \right)^3 = \left(-\frac{1}{2}\right)^3 \implies x - \frac{5}{2} = -\frac{1}{2} \implies x = 2
\]

5) Tìm x biết:
- (a) \( (x + 1)^2 = \frac{25}{144} \)

**Solution:**
\[
(x + 1)^2 = \left(\frac{5}{12}\right)^2 \implies x + 1 = \pm\frac{5}{12} \implies x = \frac{5}{12} - 1 \text{ or } x = -\frac{5}{12} - 1
\]

- (b) \( (2x - 3)^2 = \frac{4}{25} \)

**Solution:**
\[
(2x - 3)^2 = \left(\frac{2}{5}\right)^2 \implies 2x - 3 = \pm\frac{2}{5} \implies 2x = \frac{2}{5} + 3 \text{ or } 2x = -\frac{2}{5} + 3
\]

- (c) \( (2x - 1)^2 = \frac{1}{4} \)

**Solution:**
\[
(2x - 1)^2 = \left(\frac{1}{2}\right)^2 \implies 2x - 1 = \pm\frac{1}{2} \implies 2x = \frac{1}{2} + 1 \text{ or } 2x = -\frac{1}{2} + 1
\]

These steps will guide you through solving each problem correctly.