We are asked to solve the equation $(x - 5)^2 - 10 = 0$ and express the solutions in the form $x = a \pm \sqrt{b}$, where $a$ and $b$ are integers.

1. Problem Description

We are asked to solve the equation $(x - 5)^2 - 10 = 0$ and express the solutions in the form $x = a \pm \sqrt{b}$, where $a$ and $b$ are integers.

2. Solution Steps

First, isolate the squared term:

$(x - 5)^2 = 10$

Next, take the square root of both sides:

$\sqrt{(x - 5)^2} = \pm \sqrt{10}$

$x - 5 = \pm \sqrt{10}$

Finally, isolate $x$:

$x = 5 \pm \sqrt{10}$

3. Final Answer

$x = 5 \pm \sqrt{10}$