Answer: The deal will have the effect of increasing both your surplus as well as your neighbor's
Explanation:
Assuming your neighbor accepts the deal, you would have paid $3,000 when in fact your house value had reduced by $5,000. This give you a surplus of $2,000 because you paid $2,000 less than the cost to you if your neighbor did not mow the lawn.
Your neighbor also makes a surplus because where normally it would cost them $1,000 to mow the lawn, they got $3,000. They also make a surplus of $2,000 over the cost to mow.