To determine which of the given differences results in a rational number, let's evaluate each expression:
1. **\( 5 - \sqrt{2} \)**: This expression involves the subtraction of the irrational number \(\sqrt{2}\) from the rational number 5. The result is irrational.
2. **\( \sqrt{36} - \frac{2}{3} \)**: Here, \(\sqrt{36} = 6\) is a rational number, and \(\frac{2}{3}\) is also rational. The difference \(6 - \frac{2}{3} = \frac{18}{3} - \frac{2}{3} = \frac{16}{3}\) is rational.
3. **\( \pi - 1 \)**: Since \(\pi\) is an irrational number and 1 is rational, their difference is also irrational.
4. **\( 6.2 - \sqrt{3} \)**: Here, 6.2 is rational, and \(\sqrt{3}\) is irrational, so \(6.2 - \sqrt{3}\) is irrational.
Out of these options, only the difference **\( \sqrt{36} - \frac{2}{3} \)** results in a rational number. Thus, the answer is:
**\( \sqrt{36} - \frac{2}{3} \)**