The expression \( 5 - \sqrt{3} \) can be broken down to its components involving a root. To rewrite \( \sqrt{3} \) using a rational exponent, we recognize that the square root of a number can be expressed as raising that number to the power of \( \frac{1}{2} \). Therefore:
\[ \sqrt{3} = 3^{1/2} \]
However, please note that the expression \( 5 - \sqrt{3} \) itself doesn't translate directly into a simple rational exponent without further context or simplification. The options provided seem to focus on interpreting \( \sqrt{3} \) in terms of rational exponents.
Since the expression as it stands does not match the options given, if we only interpret \( \sqrt{3} \) with rational exponents, we would consider option \( 3^{5} \) inaccurate because it doesn’t relate to \( 5 - \sqrt{3} \). Therefore, if rephrasing only \( \sqrt{3} \) where required, the direct association would be:
The most suitable option representing a rational exponent correctly is: 5 to the power of 1/3.
Thus, the transformed expression \( 5^{1/3} \) does not directly apply, however for rational exponent conversion it matches with having \( \sqrt{3} \) as part of the broader term in computation requiring further context.
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