To solve the equation \( p^2 - 8 = 17 \), we start by isolating \( p^2 \):
\[ p^2 - 8 + 8 = 17 + 8 \] \[ p^2 = 25 \]
Next, we take the square root of both sides:
\[ p = \sqrt{25} \quad \text{or} \quad p = -\sqrt{25} \] \[ p = 5 \quad \text{or} \quad p = -5 \]
From the options provided (4, 5, 6, 7, 8), the possible value of \( p \) is:
\[ \boxed{5} \]