Annual report pursuant to Section 13 and 15(d)

Description of Business, Basis of Presentation, and Significant Accounting Policies (Narrative) (Details)

v3.7.0.1
Description of Business, Basis of Presentation, and Significant Accounting Policies (Narrative) (Details)
$ / shares in Units, $ in Millions
 12 Months Ended
Jul. 13, 2017
$ / shares
May 31, 2017
USD ($)
segment
$ / shares
May 31, 2016
USD ($)
May 31, 2015
USD ($)
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    
Quarterly dividend per share | $ / shares   $ 0.46    
Allowance for doubtful accounts   $ 6.0 $ 4.2  
Accounts receivable, net of allowance for doubtful accounts   507.5 408.6  
Goodwill   657.1 657.1  
Goodwill impairment loss   0.0 0.0 $ 0.0
Direct pass-through costs   5,900.0 5,100.0 4,200.0
Maximum individual workers' compensation claims liability   1.3 1.3  
Workers' compensation insurance costs in current liabilities   18.0 13.8  
Workers' compensation insurance costs in long-term liabilities   22.3 18.4  
Maximum individual health insurance claims liability   0.3 0.3  
PEO accrued health insurance reserves in current liabilities   15.7 9.5  
Stock-based compensation costs recognized   $ 35.4 34.6 $ 31.4
Decrease in effective income tax rate   (1.50%)    
Reserve for uncertain tax positions   $ 39.2 54.2  
Excess tax benefit in income tax expense   $ 18.3    
Diluted earnings per share increase | $ / shares   $ 0.05    
Subsequent Event [Member]        
Accounting Policies [Line Items]        
Declared date Jul. 13, 2017      
Quarterly dividend per share increase | $ / shares $ 0.04      
Quarterly dividend percentage increase 9.00%      
Quarterly dividend per share | $ / shares $ 0.50      
Payable date Aug. 24, 2017      
Record date Aug. 01, 2017      
Trade Receivables [Member]        
Accounting Policies [Line Items]        
Accounts receivable, net of allowance for doubtful accounts   $ 255.0 221.6  
Purchased Receivables [Member]        
Accounting Policies [Line Items]        
Accounts receivable, net of allowance for doubtful accounts   $ 252.5 $ 187.0  
Software Development [Member]        
Accounting Policies [Line Items]        
Estimated useful lives   15 years    
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 Intangible Assets [Member]        
Accounting Policies [Line Items]        
Amortization period   3 years    
Minimum [Member] | Software [Member]        
Accounting Policies [Line Items]        
Estimated useful lives   3 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 Intangible Assets [Member]        
Accounting Policies [Line Items]        
Amortization period   12 years    
Maximum [Member] | Software [Member]        
Accounting Policies [Line Items]        
Estimated useful lives   5 years    
Germany [Member] | Total Revenue [Member] | Geographic Concentration Risk [Member]        
Accounting Policies [Line Items]        
Percentage of total revenue less than one percent   1.00% 1.00% 1.00%