Solve the quadratic equation by using the square root property. (Enter your answers as a comma-separated list.) \[ \begin{array}{r} (x-5)^{2}=6 \\ x=\square \end{array} \]

Step 1 ：Given the quadratic equation \((x-5)^{2}=6\).

Step 2 ：Apply the square root property to both sides of the equation. The square root property states that if \(x^2 = a\), then \(x = \sqrt{a}\) or \(x = -\sqrt{a}\).

Step 3 ：So, \(x-5 = \sqrt{6}\) or \(x-5 = -\sqrt{6}\).

Step 4 ：Solving for \(x\) in both equations gives us two roots.

Step 5 ：Root1 is \(x = 5 + \sqrt{6}\) which simplifies to \(x = 7.449489742783178\).

Step 6 ：Root2 is \(x = 5 - \sqrt{6}\) which simplifies to \(x = 2.550510257216822\).

Step 7 ：Final Answer: The solutions to the equation are \(x = \boxed{7.449489742783178}\) and \(x = \boxed{2.550510257216822}\).