1. The problem is to calculate the division of two fractions: $\frac{5}{14} \div \frac{15}{7}$.\n\n2. The formula for dividing fractions is to multiply the first fraction by the reciprocal of the second fraction: $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}.$$\n\n3. Applying this rule, we get: $$\frac{5}{14} \times \frac{7}{15}.$$\n\n4. Multiply the numerators and denominators: $$\frac{5 \times 7}{14 \times 15} = \frac{35}{210}.$$\n\n5. Simplify the fraction by finding the greatest common divisor (GCD) of 35 and 210, which is 35.\n\n6. Cancel the common factor 35: $$\frac{\cancel{35}}{\cancel{210}} = \frac{1}{6}.$$\n\n7. Therefore, the simplest form of $\frac{5}{14} \div \frac{15}{7}$ is $\frac{1}{6}$.