$$
\begin{array}{l}
\log _{\frac{1}{2}}\left(\log _{2} x\right)=\log _{\frac{1}{3}}\left(\log _{3} y\right)=\log _{\frac{1}{5}}\left(\log _{5} z\right)=1 \Rightarrow x=2^{\frac{1}{2}}, y=3^{\frac{1}{3}}, z=5^{\frac{1}{5}} . \\
\text { Therefore } x^{6}=825=z^{10} \Rightarrow x>z \Rightarrow z<x<y .
\end{array}
$$

So the answer is $A$.
3. If $\log _{2}\left[\log _{\frac{1}{2}}\left(\log _{2} x\right)\right]=\log _{3}\left[\log _{\frac{1}{3}}\left(\log _{3} y\right)\right]=\log _{5}\left[\log _{\frac{1}{5}}\left(\log _{5} z\right)\right]=0$, then
A. $z<x<y$
B. $x<y<z$
C. $y<z<x$
D. $z<y<x$