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does the K-1 get filed with my 2017 taxes?"
You should file the K-1 you received with your 2017 income tax return if the K-1 shows a tax year ending date (look at the top of your K-1) in 2017.
You indicated that the K-1 uses "calendar year May 2016 - May 2017", which is contradictory since the 2016 calendar year ended on 12/31/2016 (it is also the wrong time frame for a fiscal year as that needs to be 12 months or less and must end on the last day of the month, e.g., beginning May 1, 2016 and ending April 30, 2017).
The yield here is the disbursement date is irrelevant; you need to amend your 2016 return if the K-1 is for calendar year 2016 or you need to report information from the K-1 on your 2017 income tax return if the K-1 has an ending date in 2017.
