To find the difference of $\frac{5}{9}-\frac{4}{27}$, the numerator and denominator of the fraction $\frac{5}{9}$ should be multiplied by so that the fractions have like denominators.
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Final Answer: The numerator and denominator of the fraction $\frac{5}{9}$ should be multiplied by $\boxed{3}$.

Steps

Step 1 ：To find the difference of $\frac{5}{9}-\frac{4}{27}$, we need to find a common denominator for the two fractions.

Step 2 ：The least common multiple (LCM) of the denominators 9 and 27 is 27.

Step 3 ：Therefore, we need to multiply the numerator and denominator of the fraction $\frac{5}{9}$ by 3 to get a denominator of 27.

Step 4 ：Final Answer: The numerator and denominator of the fraction $\frac{5}{9}$ should be multiplied by $\boxed{3}$.