In the middle of the school year, $40\%$ of Poolesville magnet students decided to transfer to the Blair magnet, and $5\%$ of the original Blair magnet students transferred to the Poolesville magnet. If the Blair magnet grew from $400$ students to $480$ students, how many students does the Poolesville magnet have after the transferring has occurred?
1. **Determine the number of students who transferred from Blair to Poolesville:**
   - Blair magnet originally had 400 students.
   - 5% of Blair students transferred to Poolesville.
   \[
   0.05 \times 400 = 20 \text{ students}
   \]

2. **Determine the number of students who transferred from Poolesville to Blair:**
   - Blair magnet grew from 400 to 480 students, an increase of 80 students.
   - Since 20 students transferred from Blair to Poolesville, the net increase in Blair students due to transfers from Poolesville is:
   \[
   80 + 20 = 100 \text{ students}
   \]

3. **Calculate the original number of Poolesville students:**
   - Let \( P \) be the original number of Poolesville students.
   - 40% of Poolesville students transferred to Blair.
   \[
   0.40P = 100 \implies P = \frac{100}{0.40} = 250
   \]

4. **Calculate the number of students remaining in Poolesville after the transfer:**
   - Poolesville lost 40% of its students to Blair.
   \[
   0.40 \times 250 = 100 \text{ students}
   \]
   - Therefore, the number of students remaining in Poolesville is:
   \[
   250 - 100 = 150
   \]
   - Additionally, Poolesville gained 20 students from Blair.
   \[
   150 + 20 = 170
   \]

Thus, the number of students in the Poolesville magnet after the transfers is \(\boxed{170}\).