To solve the problem, we first convert the mixed numbers into improper fractions. The first fraction is 5/4 and the second fraction is 5/9. We then multiply these two fractions together. The multiplication of fractions involves multiplying the numerators together and the denominators together. Thus, we have (5 * 5) / (4 * 9) = 25/36. Finally, we check if the fraction can be simplified further, but since 25 and 36 have no common factors other than 1, the fraction is already in its simplest form.