We are given a demand function $x = 200 - p - \frac{4p}{p + 3}$ and the price $p = 5$. The goal is to find the rate of change of the demand $x$ with respect to the price $p$, which means finding $\frac{dx}{dp}$, and then evaluate it at $p = 5$.

Steps:

1. Differentiate the function $x(p)$ with respect to $p$.
2. Plug in the value $p = 5$.
3. Round the answer to two decimal places.

Let me calculate this.The rate of change of the demand $x$ with respect to the price $p$ at $p = 5$ is approximately $-1.19$ units per dollar.

Would you like any further details or have any questions?

Here are 5 related questions you might find interesting:

1. How does the rate of change vary for different prices?
2. What is the significance of a negative rate of change in demand?
3. Can the demand function have a positive rate of change for some values of $p$?
4. How would the demand change if $p = 10$?
5. What happens to the rate of change as $p \to \infty$?

Tip: When differentiating a function, remember that terms like $\frac{4p}{p + 3}$ require the use of the quotient rule.