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Income Taxes and Other Taxes (Details) - USD ($)
$ in Millions
3 Months Ended 9 Months Ended
Feb. 28, 2023
Feb. 28, 2022
Aug. 31, 2021
Feb. 28, 2023
Feb. 28, 2022
Operating Loss Carryforwards [Line Items]          
Effective income tax rate (percentage) 26.30% 23.70%   36.30% 19.70%
Proceeds from income tax refunds $ 9.8        
Sales Tax          
Operating Loss Carryforwards [Line Items]          
Tax adjustments, settlements, and unusual provisions 1.8        
Tax Years 2015 to 2020          
Operating Loss Carryforwards [Line Items]          
Income taxes receivable 11.9     $ 11.9  
Employee Retention Credits          
Operating Loss Carryforwards [Line Items]          
Income taxes receivable $ 9.3     $ 9.3  
Carry Back of Net Operating Losses          
Operating Loss Carryforwards [Line Items]          
Proceeds from income tax refunds     $ 63.1