Let's solve each of the inequalities one by one.

### a) \( 7 - 5x < 52 \)

1. Start by isolating \( x \):
\[
7 - 5x < 52
\]
2. Subtract 7 from both sides:
\[
-5x < 52 - 7 \\
-5x < 45
\]
3. Divide both sides by -5 (remember to flip the inequality sign):
\[
x > -9
\]

### b) \( 4 - 3x \geq 7x + 8 \)

1. Move all terms involving \( x \) to one side:
\[
4 - 8 \geq 7x + 3x \\
-4 \geq 10x
\]
2. Divide by 10:
\[
-\frac{4}{10} \geq x \\
-\frac{2}{5} \geq x \quad \text{or} \quad x \leq -\frac{2}{5}
\]

### c) \( 5x + 7 > 3x - (15 + 2x) \)

1. Simplify the inequality:
\[
5x + 7 > 3x - 15 - 2x \\
5x + 7 > 3x - 2x - 15 \\
5x + 7 > x - 15
\]
2. Move \( x \) to the left side:
\[
5x - x > -15 - 7 \\
4x > -22
\]
3. Divide by 4:
\[
x > -\frac{22}{4} \\
x > -\frac{11}{2} \\
x > -5.5
\]

### Summary of Solutions
- a) \( x > -9 \)
- b) \( x \leq -\frac{2}{5} \)
- c) \( x > -5.5 \)