To evaluate $g(p+5)$ for $g(z) = z^2 + 8z + 10$, we need to substitute $z = p + 5$ into the expression.

1. Substitute $z = p + 5$ into $g(z)$:

   $g(p+5) = (p+5)^2 + 8(p+5) + 10$

2. Expand $(p+5)^2$:

   $(p+5)^2 = p^2 + 10p + 25$

3. Expand $8(p+5)$:

   $8(p+5) = 8p + 40$

4. Substitute these expansions back into the expression:

   $g(p+5) = p^2 + 10p + 25 + 8p + 40 + 10$

5. Combine like terms:

   $g(p+5) = p^2 + 18p + 75$

Thus, the result is:

$g(p+5) = p^2 + 18p + 75$

Would you like further explanation on any step?

Here are related questions for practice:

1. What is $g(p-3)$ for the same function $g(z) = z^2 + 8z + 10$?
2. How would you find $g(2p)$?
3. What is the derivative of $g(z) = z^2 + 8z + 10$?
4. How would $g(z)$ change if the constant term were different?
5. What is the value of $g(p+5)$ if $p = 3$?

Tip: When substituting variables, expand terms carefully to avoid calculation errors with each distribution step.