The given equation from the image is:

$p(x) = (x + 7)^2 - 15$

You mentioned that $x = 5$, so we will substitute $x = 5$ into the equation and solve for $p(5)$.

Let's calculate it step by step:

$p(5) = (5 + 7)^2 - 15$

Now, simplifying inside the parentheses:

$p(5) = (12)^2 - 15$

Next, square the 12:

$p(5) = 144 - 15$

Finally, subtract 15 from 144:

$p(5) = 129$

So, the value of $p(5)$ is 129.

Would you like further details or have any questions?

Here are some related questions to expand on this concept:

1. What happens to the function if $x = -7$?
2. How can you find the vertex of the quadratic function $p(x) = (x + 7)^2 - 15$?
3. What are the roots (solutions) of the equation $p(x) = 0$?
4. How does the graph of this quadratic function look like?
5. What is the general form of a quadratic function, and how does it relate to this one?

Tip: For quadratic functions in the form $(x + a)^2 + b$, the vertex of the parabola is at the point $(-a, b)$.