#### Answer

The solution is $x=9$

#### Work Step by Step

$\sqrt{x}-\sqrt{x-5}=1$
Take $\sqrt{x-5}$ to the right side:
$\sqrt{x}=1+\sqrt{x-5}$
Square both sides:
$(\sqrt{x})^{2}=(1+\sqrt{x-5})^{2}$
$x=1+2\sqrt{x-5}+x-5$
Leave the square root alone on the right side:
$x-1-x+5=2\sqrt{x-5}$
$4=2\sqrt{x-5}$
Take $2$ to divide the left side:
$\dfrac{4}{2}=\sqrt{x-5}$
$2=\sqrt{x-5}$
Square both sides:
$2^{2}=(\sqrt{x-5})^{2}$
$4=x-5$
Rearrange:
$x-5=4$
Solve for $x$:
$x=4+5$
$x=9$
The solution is $x=9$