1. The problem is to compare the two fractions $\frac{5}{8}$ and $\frac{2}{3}$ to determine which is greater. 2. To compare fractions, we can find a common denominator or cross-multiply. 3. Using cross-multiplication: multiply numerator of first fraction by denominator of second and vice versa. 4. Calculate $5 \times 3 = 15$ and $2 \times 8 = 16$. 5. Since $15 < 16$, it means $\frac{5}{8} < \frac{2}{3}$. 6. Therefore, $\frac{2}{3}$ is greater than $\frac{5}{8}$.