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Stock-Based Compensation - Narrative (Details) - USD ($)
$ / shares in Units, $ in Millions
12 Months Ended
May 31, 2019
May 31, 2018
May 31, 2017
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) $ 43.71 $ 37.62 $ 23.34  
Intrinsic value of options exercised $ 193.6 $ 110.9 $ 76.5  
Proceeds from stock options exercised 65.4 41.8 31.9  
Fair value of vested stock options 22.4 17.9 12.7  
Aggregate intrinsic value of outstanding options 804.7      
Aggregate intrinsic value of exercisable options $ 322.1      
Weighted-average remaining contractual term of stock options exercisable 4 years 2 months      
Unrecognized compensation cost related to unvested stock options and restricted stock $ 253.8      
Weighted-average period of time unrecognized compensation cost will be recognized 1 year 11 months      
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) 8,230,432      
Stock Compensation Plan | Continuing Operations        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Share-based compensation $ 139.2 110.7 87.5  
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 $ 34.0 $ 32.3 $ 32.5  
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