Answer:
You should pay your neighbor any amount higher than $300 and lower than $500 so that he cuts the tree down.
Step-by-step explanation:
Under the Coase Theorem both parties will seek an economical solution without regarding the initial property rights.
This means that it doesn't matter if it's your neighbor's tree that bothers you, what matters is that you don't want to be bothered anymore. You value removing the tree at $500, and your neighbor values his tree at $300. So an economically optimal solution to this dispute would be for you to pay your neighbor more than $300 but less than $500.