6. $a, b, c, d, e$ are 5 elements randomly selected from the set $\{1,2,3,4,5\}$ (repetition allowed). Then the probability that $a b c d + e$ is odd is $\qquad$
$a b c d+e=$ odd
$\Leftrightarrow a b c d=$ odd, $e=$ even;
or $a b c d=$ even, $e=$ odd.
$a b c d$ being odd has $3^{4}=81$ possibilities, $a b c d$ being even has $5^4-3^{4}=544$ possibilities. Therefore, the required probability is
$$
P=\frac{81 \times 2+544 \times 3}{5^{5}}=\frac{1794}{3125} .
$$