Simplify the expression sqrt((5-sqrt(7))/(3-sqrt(7))) - sqrt(7)

1. Rationalize the denominator of the fraction inside the square root:
\(\frac{5-\sqrt{7}}{3-\sqrt{7}} \times \frac{3+\sqrt{7}}{3+\sqrt{7}} = \frac{15 + 5\sqrt{7} - 3\sqrt{7} - 7}{9 - 7} = \frac{8 + 2\sqrt{7}}{2} = 4 + \sqrt{7}\).
2. The expression becomes \(\sqrt{4+\sqrt{7}} - \sqrt{7}\).
3. This expression cannot be simplified further into a simpler radical form without approximation.