To find the domain of the function f(x), we need to determine the values of x that make the expression inside the square root non-negative.

For the expression under the square root to be non-negative, we must have:

(1 - x)(1 + 5x) ≥ 0

Now, we need to find the critical points of the inequality, which occur when either factor is equal to zero:

1 - x = 0 => x = 1
1 + 5x = 0 => x = -1/5

These critical points divide the real number line into three intervals: (-∞, -1/5), (-1/5, 1), and (1, ∞).

Now, we can test a value in each interval to see if the inequality holds true:

For x = -2: (1 - (-2))(1 + 5(-2)) = (3)(-9) < 0 (not ≥ 0)
For x = 0: (1 - 0)(1 + 5(0)) = 1 ≥ 0
For x = 2: (1 - 2)(1 + 5(2)) = (-1)(10) < 0 (not ≥ 0)

Since the inequality holds for the interval (-1/5, 1), the domain of the function f(x) is (-1/5, 1).