The expression \(\sqrt{5^3}\) can be rewritten using the properties of exponents.
The square root can be expressed as an exponent of \(\frac{1}{2}\), so we have:
\[ \sqrt{5^3} = (5^3)^{\frac{1}{2}}. \]
Now, by using the power of a power rule, which states that \((a^m)^n = a^{m \cdot n}\), we can simplify this further:
\[ (5^3)^{\frac{1}{2}} = 5^{3 \cdot \frac{1}{2}} = 5^{\frac{3}{2}}. \]
Thus, the rational exponent in factored form is:
\[ \frac{3}{2} = \frac{3}{1} \cdot \frac{1}{2}. \]
So, the answer in factored form is:
\[ \frac{3}{1} \cdot \frac{1}{2}. \]