1. The problem is to simplify the expression $\frac{5}{\sqrt{2}}$. 2. To simplify a fraction with a square root in the denominator, we multiply numerator and denominator by the conjugate or the same root to rationalize the denominator. 3. Multiply numerator and denominator by $\sqrt{2}$: $$\frac{5}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{5 \times \sqrt{2}}{\sqrt{2} \times \sqrt{2}}$$ 4. Simplify the denominator using the property $\sqrt{a} \times \sqrt{a} = a$: $$\frac{5 \times \sqrt{2}}{\cancel{\sqrt{2}} \times \cancel{\sqrt{2}}} = \frac{5 \sqrt{2}}{2}$$ 5. The simplified form of $\frac{5}{\sqrt{2}}$ is $\frac{5 \sqrt{2}}{2}$. This is the final answer.