To solve the equation \((x - 4)^2 = 25\) using square roots, we start by taking the square root of both sides. This gives us:
\[ x - 4 = \pm 5 \]
Now we can split this into two separate equations to solve for \(x\):
- \(x - 4 = 5\)
- \(x - 4 = -5\)
For the first equation:
\[ x - 4 = 5 \] Adding 4 to both sides, we get:
\[ x = 5 + 4 = 9 \]
For the second equation:
\[ x - 4 = -5 \] Again, adding 4 to both sides, we have:
\[ x = -5 + 4 = -1 \]
Thus, the solutions to the equation \((x - 4)^2 = 25\) are:
\[ x = 9 \quad \text{and} \quad x = -1 \]
In conclusion, the final solutions are:
\(\boxed{9}\) and \(\boxed{-1}\)