5. The elements of set $A$ are positive integers, with the property: if $a \in A$, then $42-a \in A$. Therefore, the number of such sets $A$ is $\qquad$.

Translating the text into English while preserving the original formatting and line breaks, the result is as follows:

5. The elements of set $A$ are positive integers, with the property: if $a \in A$, then $42-a \in A$. Therefore, the number of such sets $A$ is $\qquad$.
$5.2^{21}-1$  
It is easy to know that $A$ is a subset of $\{1,2, \cdots, 41\}$, and let $C=$ $\{(1,41),(2,39),(3,38), \cdots,(20,22)\}$. If the number of elements in $A$ is even, we only need to take several pairs from $C$, the number of ways to take is $2^{20}$ -1; if the number of elements in $A$ is odd, then $21 \in A$, the number of ways to take is $2^{20}$. According to the principle of addition, the number of sets that satisfy the condition is $2^{21}-1$.