5. Let any real numbers $a>b>c>d>0$. To make
$$
\begin{array}{l}
\log _{\frac{b}{a}} 2014+\log _{\frac{d}{b}} 2014+\log _{\frac{d}{c}} 2014 \\
\geqslant m \log _{\frac{d}{a}} 2014
\end{array}
$$

always hold, then the minimum value of $m$ is $\qquad$.
5.9.
$$
\begin{array}{l}
\text { Let } x_{1}=-\log _{2014} \frac{b}{a}, x_{2}=-\log _{2014} \frac{c}{b}, \\
x_{3}=-\log _{2014} \frac{d}{c} .
\end{array}
$$

Since $a>b>c>d>0$, we have
$$
x_{1}>0, x_{2}>0, x_{3}>0 \text {. }
$$

Thus, the given inequality can be transformed into
$$
\begin{array}{l}
\frac{1}{x_{1}}+\frac{1}{x_{2}}+\frac{1}{x_{3}} \leqslant m \cdot \frac{1}{x_{1}+x_{2}+x_{3}} \\
\Rightarrow m \geqslant\left(x_{1}+x_{2}+x_{3}\right)\left(\frac{1}{x_{1}}+\frac{1}{x_{2}}+\frac{1}{x_{3}}\right) \geqslant 9 .
\end{array}
$$

When $x_{1}=x_{2}=x_{3}$, i.e., $a, b, c, d$ form a geometric sequence, the equality holds.
Therefore, the minimum value of $m$ is 9.