6. Replace the letters with digits to get a true equality: $\overline{13 a b c d e}: 5=\overline{a b c d e 6}$.
First method:

We have $\overline{a b c d e 6} \cdot 5=\overline{13 a b c d e} . \quad 1$ POINT

By multiplying $\overline{a b c d e 6} \cdot 5$ we will gradually reveal the digits $a, b, c, d, e . \quad 1$ POINT

$5 \cdot 6=30$ so $e=0 . \quad 1$ POINT

$5 \cdot 0+3=3$ so $d=3 . \quad 1$ POINT

$5 \cdot 3+0=15$ so $c=5 . \quad 1$ POINT

$5 \cdot 5+1=26$ so $b=6$. 1 POINT

$5 \cdot 6+2=32$ so $a=2$. 1 POINT

$5 \cdot 2+3=13$. 1 POINT

$1326530: 5=265306 \quad 2$ POINTS

TOTAL 10 POINTS