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Description of Business, Basis of Presentation, and Significant Accounting Policies (Narrative) (Details)
$ in Millions
 3 Months Ended 12 Months Ended
Aug. 31, 2023
USD ($)
Item
Segment
Aug. 31, 2022
USD ($)
Item
May 31, 2024
USD ($)
May 31, 2023
USD ($)
Item
Accounting Policies [Line Items]        
Number of reportable segments | Segment 1      
Allowance for credit losses $ 20.8     $ 20.5
Advance collections 28.2     12.5
Maximum individual health insurance claims liability       0.5
Stock-based compensation costs recognized $ 16.0 $ 14.4    
Accounting Standards Update 2021-08 [Member]        
Accounting Policies [Line Items]        
Change in accounting principle, accounting standards update, adoption date Jun. 01, 2023      
Change in accounting principle, accounting standards update, adopted [true false] true      
Change in accounting principle, accounting standards update, immaterial effect [true false] true      
Forecast [Member]        
Accounting Policies [Line Items]        
Maximum individual health insurance claims liability     $ 0.5  
Trade Receivables [Member]        
Accounting Policies [Line Items]        
Receivables $ 200.8     287.0
Purchased Receivables [Member]        
Accounting Policies [Line Items]        
Receivables $ 835.8     $ 606.8
Accounts And Unbilled Receivables [Member]        
Accounting Policies [Line Items]        
Number of clients creating a credit concentration | Item 0     0
Revenue [Member]        
Accounting Policies [Line Items]        
Number of clients creating a credit concentration | Item 0 0    
PEO Aggregate Claims Exceeding $1.0M [Member] | Minimum [Member]        
Accounting Policies [Line Items]        
Individual workers' compensation claims liability       $ 1.0
PEO Aggregate Claims Exceeding $1.0M [Member] | Minimum [Member] | Forecast [Member]        
Accounting Policies [Line Items]        
Individual workers' compensation claims liability     1.0  
PEO Aggregate Claims Exceeding $1.0M [Member] | Maximum [Member]        
Accounting Policies [Line Items]        
Maximum individual workers' compensation claims liability       $ 2.0
PEO Aggregate Claims Exceeding $1.0M [Member] | Maximum [Member] | Forecast [Member]        
Accounting Policies [Line Items]        
Maximum individual workers' compensation claims liability     $ 1.0