In the expression $$\frac{5}{7}\div\frac{6}{7}$$ the denominator of the numerator and the denominator of the denominator gets cancelled.
Hence the expression can be written as $$\frac{5}{6}$$
$$\frac{1}{5}\times\frac{5}{6}$$=$$\frac{1}{6}$$
Hence Option C is the correct Answer.
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