(10 Given $\lg x_{1}, \lg x_{2}, \lg x_{3}, \lg x_{4}, \lg x_{5}$ are consecutive positive integers (in ascending or descending order), and $\left(\lg x_{4}\right)^{2}<\lg x_{1} \cdot \lg x_{5}$, then the minimum value of $x_{1}$ is $\qquad$ .
(10) If $x_{1}\frac{5}{2}$, so $k \geqslant$
3. Thus $\lg x_{1}=k+2 \geqslant 5, x_{1} \geqslant 100000$. When $x_{1}=100000$, $x_{2}=10000$, $x_{3}=1000, x_{4}=100, x_{5}=10$, so the minimum value of $x_{1}$ is 100000.