The correct answer is $\boxed{\text{A}}$.
In the given question, we are given the following information:
- $B5D$ means $B$ is the father of $D$.
- $B9D$ means $B$ is the sister of $D$.
- $B4D$ means $B$ is the brother of $D$.
- $B3D$ means $B$ is the wife of $D$.
We are asked to find the option that means $F$ is the mother of $K$.
Looking at the options, we can see that $\text{A}$ is the only option that satisfies the given conditions. In $\text{A}$, $F$ is followed by $3$, which means $F$ is the parent of $K$. The only parent relationship that is consistent with this is that $F$ is the mother of $K$.
The other options do not satisfy the given conditions. In $\text{B}$, $F$ is followed by $5$, which means $F$ is the child of $K$. However, we know that $F$ is the parent of $K$, so this cannot be the correct answer. In $\text{C}$, $F$ is followed by $9$, which means $F$ is the sibling of $K$. However, we know that $F$ is the parent of $K$, so this cannot be the correct answer. In $\text{D}$, $F$ is followed by $3$ and $5$, which means $F$ is both the parent and the child of $K$. This is not possible, so this cannot be the correct answer.
Therefore, the correct answer is $\boxed{\text{A}}$.