Let's solve the given equation step by step.

The equation is:

$-3 - \frac{3}{4}(c - 4) = \frac{5}{4}$

Step 1: Distribute $\frac{3}{4}$ on the left-hand side:

$-3 - \frac{3}{4}c + \frac{3}{4} \times 4 = \frac{5}{4}$

Simplifying: $-3 - \frac{3}{4}c + 3 = \frac{5}{4}$

Step 2: Combine like terms:

$- \frac{3}{4}c = \frac{5}{4}$

Step 3: Multiply both sides by $-\frac{4}{3}$ to solve for $c$:

$c = \frac{5}{4} \times \left(-\frac{4}{3}\right)$

$c = -\frac{20}{12} = -\frac{5}{3}$

So, the value of $c$ is $-\frac{5}{3}$.

The correct answer is $-\frac{5}{3}$, which matches one of the options in the box.

Would you like more details on any step, or do you have any questions?

Here are some related questions to explore:

1. How do you solve equations with fractions more efficiently?
2. What happens if you have fractions on both sides of the equation?
3. Can you explain how to factor out common terms when solving equations?
4. How can you check your solution for equations with variables?
5. How do you solve systems of equations involving fractions?

Tip: Always simplify the equation step by step to avoid mistakes, especially when dealing with fractions.