$$(5^{-1}\div6^{-1})\times(\frac{1}{5})^{-1}$$
$6$
$$\frac{\frac{1}{5}}{6^{-1}}\times \left(\frac{1}{5}\right)^{-1}$$
$$\frac{\frac{1}{5}}{\frac{1}{6}}\times \left(\frac{1}{5}\right)^{-1}$$
$$\frac{1}{5}\times 6\times \left(\frac{1}{5}\right)^{-1}$$
$$\frac{6}{5}\times \left(\frac{1}{5}\right)^{-1}$$
$$\frac{6}{5}\times 5$$
$$6$$
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$2\times 3$
