1. The problem is to find the result of dividing $\frac{5}{4}$ by $\frac{2}{3}$. Helena made a mistake in the first step. 2. Helena's mistake was that she flipped the wrong fraction. When dividing fractions, you must multiply by the reciprocal of the divisor. The reciprocal of $\frac{2}{3}$ is $\frac{3}{2}$, not $\frac{4}{5}$. 3. The correct formula for dividing fractions is: $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$$ 4. Applying this to our problem: $$\frac{5}{4} \div \frac{2}{3} = \frac{5}{4} \times \frac{3}{2}$$ 5. Multiply the numerators and denominators: $$\frac{5 \times 3}{4 \times 2} = \frac{15}{8}$$ 6. The fraction $\frac{15}{8}$ is already in simplest form because 15 and 8 have no common factors other than 1. 7. Therefore, the correct answer is: $$\frac{15}{8}$$