1. Given real numbers $x, y, z$ satisfy:
$$
\left\{\begin{array}{l}
\log _{2}\left(x y z-6+\log _{5} x\right)=4, \\
\log _{3}\left(x y z-6+\log _{5} y\right)=3, \\
\log _{4}\left(x y z-6+\log _{5} z\right)=2 .
\end{array}\right.
$$

Then $\left|\log _{5} x\right|+\left|\log _{5} y\right|+\left|\log _{5} z\right|=$ $\qquad$
- 1. 14.

The original system of equations can be transformed into
$$
\left\{\begin{array}{l}
x y z+\log _{5} x=22, \\
x y z+\log _{5} y=33, \\
x y z+\log _{5} z=22 .
\end{array}\right.
$$

Adding the three equations yields
$$
3 x y z+\log _{5} x y z=77 \text {. }
$$

Notice that, $f(t)=3 t+\log _{5} t$ is monotonically increasing on the interval $(0,+\infty)$, and $f(25)=77$.
$$
\text { Therefore, } x y z=25 \text {. }
$$

Substituting $x y z=25$ back into the system of equations (1) gives
$$
\log _{5} x=-3, \log _{5} y=8, \log _{5} z=-3 \text {. }
$$

Thus, the required expression is $3+8+3=14$.