$\frac{3}{5}+\frac{5}{9}$

Step 1 ：Given the fractions \(\frac{3}{5}\) and \(\frac{5}{9}\)

Step 2 ：Find the least common multiple of the denominators 5 and 9, which is 45

Step 3 ：Convert each fraction into an equivalent fraction with the common denominator by multiplying the numerator and denominator of each fraction by the factor needed to change the denominator into the common denominator

Step 4 ：The equivalent fractions are \(\frac{27}{45}\) and \(\frac{25}{45}\)

Step 5 ：Add the numerators of the equivalent fractions to get the numerator of the result, and the denominator of the result is the common denominator

Step 6 ：The result of the addition of the two fractions is \(\frac{52}{45}\)

Step 7 ：This fraction cannot be simplified further as the numerator and denominator do not have any common factors other than 1

Step 8 ：Final Answer: \(\boxed{\frac{52}{45}}\)