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Income Taxes and Other Taxes (Details) - USD ($)
$ in Millions
3 Months Ended 6 Months Ended
Nov. 30, 2022
Nov. 30, 2021
Aug. 31, 2021
Nov. 30, 2022
Nov. 30, 2021
Operating Loss Carryforwards [Line Items]          
Effective income tax rate (percentage) 25.30% 23.20%   30.20% 21.10%
Tax Years 2015 to 2020          
Operating Loss Carryforwards [Line Items]          
Income taxes receivable $ 20.0     $ 20.0  
Employee Retention Credits          
Operating Loss Carryforwards [Line Items]          
Income taxes receivable $ 10.1     $ 10.1  
Carry Back of Net Operating Losses          
Operating Loss Carryforwards [Line Items]          
Proceeds from Income Tax Refunds     $ 63.1