Solve the equation by the square root property. $$ (x-5)^{2}=64 $$ What is the solution set? $$ \{ $$ (Use a comma to separate answers as needed.)

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To solve the equation $$(x - 5)^2 = 64$$ using the square root property, follow these steps:

1. **Apply the Square Root Property:**
   $$
   (x - 5)^2 = 64 \implies x - 5 = \pm \sqrt{64}
   $$
   
2. **Simplify the Square Root:**
   $$
   \sqrt{64} = 8
   $$
   So,
   $$
   x - 5 = \pm 8
   $$
   
3. **Solve for $$x$$ in Both Cases:**
   - **Case 1:** $$x - 5 = 8$$
     $$
     x = 5 + 8 = 13
     $$
   
   - **Case 2:** $$x - 5 = -8$$
     $$
     x = 5 - 8 = -3
     $$

4. **Write the Solution Set:**
   $$
   \{-3, 13\}
   $$

**Final Answer:** $$\{-3, 13\}$$
The solutions are $$ x = -3 $$ and $$ x = 13 $$.

Solve the equation by the square root property. \[ (x-5)^{2}=64 \] What is the solution set? \( \{ \) (Use a comma to separate answers as needed.)

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