The expression \( 5 - \sqrt{3} \) can be rewritten using a rational exponent. The square root can be expressed with an exponent of \( \frac{1}{2} \). Therefore:
\[ \sqrt{3} = 3^{\frac{1}{2}} \]
Since you are looking for \( 5 - \sqrt{3} \), we will just express \(\sqrt{3}\) using a rational exponent. However, if specifically asked to express something like \( 5^{-\sqrt{3}} \), you can rewrite it as:
\[ 5^{-\sqrt{3}} = 5^{-3^{\frac{1}{2}}} \]
If you just need to focus on \( \sqrt{3} \), the rational exponent form of \( \sqrt{3} \) is \( 3^{\frac{1}{2}} \).
Therefore, none of the provided responses relate directly to the specific expression \( 5 - \sqrt{3} \). Please clarify the expression you're asking about if it's different, or if there's more context needed.
For the options you provided:
- The first option (513) doesn't make sense in context.
- \( 5^{\frac{1}{3}} \) (second option) is not related as we dealt with square roots, not cube roots.
- The third option (3^5) also doesn’t relate.
- The fourth option (5 cubed) is unrelated as well.
To conclude, if you're looking strictly for a rational exponent expressing \( \sqrt{3} \), that would be \( 3^{\frac{1}{2}} \), and please correct me if you are looking for something specific related to \( 5 - \sqrt{3} \).