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Stock-Based Compensation - Narrative (Details) - USD ($)
$ / shares in Units, $ in Millions
12 Months Ended
May 31, 2016
May 31, 2015
May 31, 2014
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Weighted-average fair value of stock options granted (dollars per share) $ 21.60 $ 20.64 $ 16.63
Intrinsic value of options exercised $ 48.5 $ 44.3 $ 19.8
Proceeds from stock options exercised 28.2 40.2 41.9
Fair value of vested stock options 11.0 10.9 17.7
Aggregate intrinsic value of outstanding options 276.5    
Aggregate intrinsic value of exercisable options $ 99.7    
Weighted-average remaining contractual term of stock options exercisable 4 years 8 months 6 days    
Unrecognized compensation cost related to unvested stock options and restricted stock $ 149.4    
Weighted-average period of time unrecognized compensation cost will be recognized 1 year 11 months 6 days    
Stock Compensation Plan      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Number of shares authorized under plan (shares) 21,000,000    
Shares reserved for future issuance (shares) 7,174,600    
Stock Compensation Plan | Continuing Operations      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Share-based compensation $ 79.3 44.9 27.5
Stock Compensation Plan | Continuing Operations | Income Taxes      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
The total income tax benefit recognized in the consolidated income statement for share-based compensation arrangements $ 28.9 $ 16.7 $ 10.2
Stock Options      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Maximum term after grant options may be exercised 10 years    
Award expiration term 10 years    
Stock Options | Minimum      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Options vesting period 3 years    
Stock Options | Maximum      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Options vesting period 5 years    
Restricted Stock Awards      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Vesting period of awards 3 years