Answer
$[-5, 5) $
Work Step by Step
Given $f(x) = \sqrt {\frac{5+x}{5-x}}$
In a even root function, the domain is defined such that the function is always at (if defined) or above 0, so $f(x) \geq 0$
$\sqrt {\frac{5+x}{5-x}} \geq 0$
$\frac{5+x}{5-x} \geq 0$
Find the zeros of the expressions in the numerator AND the denominator
$x = -5, 5$
Test numbers in between those zero values to determine if the function is negative or positive
(-∞, -5] $\frac{(-)}{(+)} = (-)$
[-5, 5) $\frac{(+)}{(+)} = (+)$
(5,∞) $\frac{(+)}{(-)} = (-)$
Thus the solution is $[-5, 5) $