To simplify the expression \(\frac{\sqrt{500}}{\sqrt{10}}\), we can start by simplifying the numerator.
First, simplify \(\sqrt{500}\):
\[ 500 = 100 \times 5 = 10^2 \times 5 \]
Thus:
\[ \sqrt{500} = \sqrt{100 \times 5} = \sqrt{100} \times \sqrt{5} = 10\sqrt{5} \]
Now, substitute this back into the original expression:
\[ \frac{\sqrt{500}}{\sqrt{10}} = \frac{10\sqrt{5}}{\sqrt{10}} \]
Next, we simplify the fraction:
\[ \frac{10\sqrt{5}}{\sqrt{10}} = 10\cdot\frac{\sqrt{5}}{\sqrt{10}} = 10\cdot\sqrt{\frac{5}{10}} = 10\cdot\sqrt{\frac{1}{2}} = 10 \cdot \frac{\sqrt{2}}{2} = 5\sqrt{2} \]
Thus, the expression in simplest radical form is:
\[ \boxed{5\sqrt{2}} \]