To solve the inequalities given:

### Part (a): \( 5x + 7 > 8x - 5 \)

1. Start by isolating the variable on one side. First, subtract \( 5x \) from both sides:
\[
7 > 8x - 5 - 5x
\]
This simplifies to:
\[
7 > 3x - 5
\]

2. Next, add \( 5 \) to both sides:
\[
7 + 5 > 3x
\]
This simplifies to:
\[
12 > 3x
\]
or
\[
3x < 12
\]

3. Now, divide both sides by \( 3 \):
\[
x < 4
\]

### Conclusion for Part (a):
The solution is:
\[ x < 4 \]

---

### Part (b): \( -4x + 3 \leq 3x - 1 \)

1. Start by isolating the variable on one side. First, add \( 4x \) to both sides:
\[
3 \leq 3x + 4x - 1
\]
This simplifies to:
\[
3 \leq 7x - 1
\]

2. Next, add \( 1 \) to both sides:
\[
3 + 1 \leq 7x
\]
This simplifies to:
\[
4 \leq 7x
\]
or
\[
7x \geq 4
\]

3. Now, divide both sides by \( 7 \):
\[
x \geq \frac{4}{7}
\]

### Conclusion for Part (b):
The solution is:
\[ x \geq \frac{4}{7} \]

### Final Summary of Solutions:
- For (a): \( x < 4 \)
- For (b): \( x \geq \frac{4}{7} \)