Dear Military Family:
New York does not provide a statute that mandates that a landlord pro rate rent.
You may inquire from the JAG at the current base if there is a federal law that overrides your lease and the law of month to month tenancies in New York.
The big problem is that you are not moving out until May 13 and in New York, the entire rent for the full month is due to the landlord on the rent due date, without any apportionment.
What is at risk if you do not pay for May? Will the landlord chase you for that one month?
You have to evaluate that on your own.
Thank you for your service and Best of Luck.
The answer provided to you is in the nature of general information. The general proposition being that you should try to avoid a bad outcome if you can.
Rent is normally not pro-rated unless a tenant becomes a holdover after termination of a lease and the Landlord requests fair value for the tenant's use and occupancy after termination.