Solve the equation. \[ (w-4)^{2}=16+5 w \]

To solve the equation \((w-4)^{2}=16+5 w\), let's start by expanding the left side: \[ (w-4)^{2} = w^{2} - 8w + 16. \] Now, we can rewrite the equation: \[ w^{2} - 8w + 16 = 16 + 5w. \] Next, subtract \(16 + 5w\) from both sides: \[ w^{2} - 8w + 16 - 16 - 5w = 0. \] This simplifies to: \[ w^{2} - 13w = 0. \] Now, factor out \(w\): \[ w(w - 13) = 0. \] Setting each factor to zero gives us: \[ w = 0 \quad \text{or} \quad w - 13 = 0 \Rightarrow w = 13. \] Thus, the solutions to the equation are: \[ w = 0 \quad \text{or} \quad w = 13. \] **Final Answer: \( w = 0 \) or \( w = 13 \)**