To solve the equation \((x-4)^2 = 5x - 20\), we can follow these steps:

1. Expand the left-hand side of the equation:
\[
(x-4)^2 = x^2 - 8x + 16
\]

2. Substitute the expanded form back into the equation:
\[
x^2 - 8x + 16 = 5x - 20
\]

3. Move all terms to one side of the equation to set it to zero:
\[
x^2 - 8x + 16 - 5x + 20 = 0
\]

4. Combine like terms:
\[
x^2 - 13x + 36 = 0
\]

5. Now, we need to solve the quadratic equation \(x^2 - 13x + 36 = 0\). We can factor it:
\[
(x - 9)(x - 4) = 0
\]

6. Set each factor equal to zero and solve for \(x\):
\[
x - 9 = 0 \quad \text{or} \quad x - 4 = 0
\]
\[
x = 9 \quad \text{or} \quad x = 4
\]

So, the solutions to the equation \((x-4)^2 = 5x - 20\) are \(x = 9\) and \(x = 4\).