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Stock-Based Compensation - Narrative (Details) - USD ($)
$ / shares in Units, $ in Millions
12 Months Ended
May 31, 2018
May 31, 2017
May 31, 2016
Aug. 02, 2016
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Weighted-average fair value of stock options granted (dollars per share) $ 29.31 $ 23.34 $ 22.20  
Intrinsic value of options exercised $ 110.9 $ 76.5 $ 48.5  
Proceeds from stock options exercised 41.8 31.9 28.2  
Fair value of vested stock options 17.9 12.7 11.0  
Aggregate intrinsic value of outstanding options 728.0      
Aggregate intrinsic value of exercisable options $ 277.6      
Weighted-average remaining contractual term of stock options exercisable 4 years 4 months      
Unrecognized compensation cost related to unvested stock options and restricted stock $ 258.6      
Weighted-average period of time unrecognized compensation cost will be recognized 1 year 10 months 24 days      
Stock Compensation Plan        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Number of shares authorized under plan (shares)       12,500,000
Shares reserved for future issuance (shares) 10,595,954      
Stock Compensation Plan | Continuing Operations        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Share-based compensation $ 110.7 87.5 77.8  
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 $ 32.3 $ 32.5 $ 28.3  
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