Let's calculate the change in temperature step by step:
- The initial temperature was 81°F.
- The temperature dropped by 9°F: \[ 81°F - 9°F = 72°F \]
- The temperature then rose by 5°F: \[ 72°F + 5°F = 77°F \]
Now, we need to determine how much the temperature needs to change to return to the initial temperature of 81°F:
\[ 81°F - 77°F = 4°F \]
Therefore, the temperature needs to rise by 4°F to return to the initial temperature of 81°F.