Step 1: Simplify the expression inside the square root in the numerator. $$ \sqrt{25-1} = \sqrt{24} $$ Step 2: Simplify the square root in the denominator. $$ \sqrt{4} = 2 $$ Step 3: Rewrite the expression with the simplified numerator and denominator. $$ \frac{\sqrt{24}}{2} $$ Step 4: Simplify $\sqrt{24}$ by finding its prime factors. $$ \sqrt{24} = \sqrt{4 \times 6} = \sqrt{4} \times \sqrt{6} = 2\sqrt{6} $$ Step 5: Substitute the simplified $\sqrt{24}$ back into the expression. $$ \frac{2\sqrt{6}}{2} $$ Step 6: Cancel out the common factor of 2 in the numerator and denominator. $$ \frac{2\sqrt{6}}{2} = \sqrt{6} $$ The final answer is $\boxed{\sqrt{6}}$.