(1) Given the set $M=\{1,3,5,7,9\}$, if the non-empty set $A$ satisfies: the elements of $A$ each increased by 4 form a subset of $M$, and the elements of $A$ each decreased by 4 also form a subset of $M$, then $A=$ $\qquad$ .
(1) $\{5\}$ Hint: Let
$$
\begin{array}{l}
M_{1}=\{x \mid x=m-4, m \in M\}=\{-3,-1,1,3,5\}, \\
M_{2}=\{x \mid x=m+4, m \in M\}=\{5,7,9,11,13\},
\end{array}
$$

From the given condition, $A \subseteq M_{1} \cap M_{2}=\{5\}$.
Since $A$ is a non-empty set, we have $A=\{5\}$.