$$3\frac{2}{5\frac{1}{5}}+5\frac{1}{5}$$
$\frac{413}{65}\approx 6.353846154$
$$3\times \frac{2\times 5}{5\times 5+1}+\frac{5\times 5+1}{5}$$
$$3\times \frac{10}{5\times 5+1}+\frac{5\times 5+1}{5}$$
$$3\times \frac{10}{25+1}+\frac{5\times 5+1}{5}$$
$$3\times \frac{10}{26}+\frac{5\times 5+1}{5}$$
$$3\times \frac{5}{13}+\frac{5\times 5+1}{5}$$
$$\frac{3\times 5}{13}+\frac{5\times 5+1}{5}$$
$$\frac{15}{13}+\frac{5\times 5+1}{5}$$
$$\frac{15}{13}+\frac{25+1}{5}$$
$$\frac{15}{13}+\frac{26}{5}$$
$$\frac{75}{65}+\frac{338}{65}$$
$$\frac{75+338}{65}$$
$$\frac{413}{65}$$
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$\frac{7 \cdot 59}{5 \cdot 13} = 6\frac{23}{65} = 6.3538461538461535$
