Since your starting date and ending date vary each year, I would just put them in manually.
IF(TempDate > 1/27/2015 AND TempDate < 1/25/2016 , 'FY2016',
IF(TempDate > 1/26/2016 AND TempDate < 1/30/2017 , 'FY2017',
IF(TempDate > 1/31/2017 AND TempDate < 1/29/2018 , 'FY2018',
IF(TempDate > 1/30/2018 AND TempDate < 1/28/2019 , 'FY2019',
IF(TempDate > 1/29/2019 AND TempDate < 1/27/2020 , 'FY2020',
IF(TempDate > 1/28/2020 AND TempDate < 1/25/2021 , 'FY2021',
IF(TempDate > 1/26/2021 AND TempDate < 1/31/2022 , 'FY2022', ))))))) AS [Fiscal Years]
Only thing here is that you should place the matching condition in the same format as your TempDate and after 2022 you will have to type the next years in the script manually again.
Let me know if this works.