First, we can rewrite the expression as a multiplication by finding the reciprocal of the second fraction:
$$\frac{5}{18} \div \frac{11}{27} = \frac{5}{18} \cdot \frac{27}{11}$$
Now, we can multiply the fractions:
$$\frac{5}{18} \cdot \frac{27}{11} = \frac{5
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