Rio likes fruit, and one day she decides to pick persimmons. She picks a total of $12$ persimmons from the first $5$ trees she sees. Rio has $5$ more trees to pick persimmons from. If she wants to pick an average of $4$ persimmons per tree overall, what is the average number of persimmons that she must pick from each of the last $5$ trees for her goal?
1. Rio picks a total of $12$ persimmons from the first $5$ trees.
2. She wants to pick an average of $4$ persimmons per tree overall. Since there are $10$ trees in total, the total number of persimmons she wants to pick is:
   \[
   4 \text{ persimmons/tree} \times 10 \text{ trees} = 40 \text{ persimmons}
   \]
3. She has already picked $12$ persimmons from the first $5$ trees. Therefore, the number of persimmons she still needs to pick from the remaining $5$ trees is:
   \[
   40 \text{ persimmons} - 12 \text{ persimmons} = 28 \text{ persimmons}
   \]
4. To find the average number of persimmons she must pick from each of the last $5$ trees, we divide the remaining persimmons by the number of trees:
   \[
   \frac{28 \text{ persimmons}}{5 \text{ trees}} = \frac{28}{5} \text{ persimmons/tree}
   \]

The final answer is $\boxed{\frac{28}{5}}$ persimmons/tree.