The derivative of the demand function $x$ with respect to the price $p$ is:

$\frac{dx}{dp} = \frac{4p}{(p + 2)^2} - 1 - \frac{4}{p + 2}$

Now, let's compute the rate of change at $p = 5$.It seems like I can’t do more advanced data analysis right now. Please try again later. However, you can substitute $p = 5$ directly into the derivative equation:

$\frac{dx}{dp} = \frac{4(5)}{(5 + 2)^2} - 1 - \frac{4}{5 + 2}$

This will give you the rate of change in the demand $x$ when the price $p$ is 5.

Would you like further clarification on this, or have any other questions? Here are some related questions:

1. How does the demand function change as the price increases or decreases?
2. What is the economic interpretation of $\frac{dx}{dp}$?
3. How does the presence of the term $\frac{4p}{p + 2}$ affect the demand?
4. What does it mean for the rate of change to be negative?
5. How would the rate of change vary if the price $p$ were different?

Tip: When dealing with derivatives in economics, the sign of the derivative often tells you whether a quantity is increasing or decreasing with respect to the variable.