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Description of Business, Basis of Presentation, and Significant Accounting Policies (Narrative) (Details)
$ / shares in Units, $ in Millions
 12 Months Ended
Jul. 12, 2018
$ / shares
May 31, 2018
USD ($)
segment
May 31, 2017
USD ($)
May 31, 2016
USD ($)
Accounting Policies [Line Items]        
Number of reportable segments | segment   1    
Maximum period in which payroll taxes will be remitted after receipt of collections from clients   90 days    
Goodwill   $ 814.0 $ 657.1  
Goodwill impairment loss   0.0 0.0 $ 0.0
Direct pass-through costs   7,900.0 5,900.0 $ 5,100.0
Maximum individual workers' compensation claims liability   1.3 1.3  
Workers' compensation insurance costs in current liabilities   19.4 18.0  
Workers' compensation insurance costs in long-term liabilities   31.2 22.3  
Maximum individual health insurance claims liability   0.3 0.3  
PEO accrued health insurance reserves in current liabilities   25.4 15.7  
Reserve for uncertain tax positions   $ 14.7 $ 39.2  
Subsequent Event [Member]        
Accounting Policies [Line Items]        
Declared date Jul. 12, 2018      
Quarterly dividend per share | $ / shares $ 0.56      
Payable date Aug. 23, 2018      
Record date Aug. 01, 2018      
Minimum [Member]        
Accounting Policies [Line Items]        
Period in which payroll taxes are typically remitted after receipt of collections from clients   1 day    
Payroll funding fees average collection period   35 days    
Minimum [Member] | Finite Lived Assets [Member]        
Accounting Policies [Line Items]        
Amortization period   3 years    
Minimum [Member] | Software [Member]        
Accounting Policies [Line Items]        
Estimated useful lives   3 years    
Minimum [Member] | Software Development [Member]        
Accounting Policies [Line Items]        
Estimated useful lives   12 years    
Maximum [Member]        
Accounting Policies [Line Items]        
Period in which payroll taxes are typically remitted after receipt of collections from clients   30 days    
Payroll funding fees average collection period   45 days    
Short-term investments maturity at acquisition   90 days    
Maximum [Member] | Finite Lived Assets [Member]        
Accounting Policies [Line Items]        
Amortization period   12 years    
Maximum [Member] | Software [Member]        
Accounting Policies [Line Items]        
Estimated useful lives   5 years    
HR Outsourcing Holdings, Inc. [Member]        
Accounting Policies [Line Items]        
Maximum individual workers' compensation claims liability   $ 0.5    
Maximum individual health insurance claims liability   $ 0.3    
Europe [Member] | Revenue [Member] | Geographic Concentration Risk [Member] | Maximum [Member]        
Accounting Policies [Line Items]        
Total percentage   1.00% 1.00% 1.00%
Europe [Member] | Long Lived Assets [Member] | Geographic Concentration Risk [Member]        
Accounting Policies [Line Items]        
Total percentage   13.00%