#### Answer

Fill the blanks in this order:
$\pm\sqrt{5}$,
$7\pm\sqrt{5}$,
$\sqrt{5}$,
$\sqrt{5}$.

#### Work Step by Step

$(x-7)^{2}=5\qquad$...use the principle of square roots.
$ x-7=\pm\sqrt{5}\qquad$...add $7$ to both sides.
$x=7\pm\sqrt{5}$
The solutions are $7+\sqrt{5}$ and $7-\sqrt{5}$