$$\frac{5}{5-\frac{1}{5-\frac{1}{5}}}$$
$\frac{24}{23}\approx 1.043478261$
$$\frac{5}{5-\frac{1}{\frac{25}{5}-\frac{1}{5}}}$$
$$\frac{5}{5-\frac{1}{\frac{25-1}{5}}}$$
$$\frac{5}{5-\frac{1}{\frac{24}{5}}}$$
$$\frac{5}{5-1\times \frac{5}{24}}$$
$$\frac{5}{5-\frac{5}{24}}$$
$$\frac{5}{\frac{120}{24}-\frac{5}{24}}$$
$$\frac{5}{\frac{120-5}{24}}$$
$$\frac{5}{\frac{115}{24}}$$
$$5\times \frac{24}{115}$$
$$\frac{5\times 24}{115}$$
$$\frac{120}{115}$$
$$\frac{24}{23}$$
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$\frac{2 ^ {3} \cdot 3}{23} = 1\frac{1}{23} = 1.0434782608695652$
