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Stock-Based Compensation - Narrative (Details) - USD ($)
$ / shares in Units, $ in Millions
12 Months Ended
May 31, 2022
May 31, 2021
May 31, 2020
Aug. 02, 2016
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Weighted-average fair value of stock options granted (in dollars per share) $ 84.10 $ 66.52 $ 48.20  
Intrinsic value of options exercised $ 348.3 $ 402.3 $ 262.1  
Proceeds from stock options exercised 117.7 130.0 90.5  
Fair value of vested stock options 36.7 30.5 27.8  
Aggregate intrinsic value of outstanding options 853.2      
Aggregate intrinsic value of exercisable options $ 443.0      
Weighted-average remaining contractual term of stock options exercisable 4 years      
Unrecognized compensation cost related to unvested stock options and restricted stock $ 221.8      
Weighted-average period of time unrecognized compensation cost will be recognized 2 years 1 month 13 days      
Stock Compensation Plan        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Number of shares authorized under plan (in shares)       12,500,000
Shares reserved for future issuance (in shares) 5,966,288      
Stock Compensation Plan | Continuing Operations        
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]        
Share-based compensation $ 109.3 112.0 115.4  
The total income tax benefit recognized in the consolidated income statement for share-based compensation arrangements $ 27.9 $ 28.6 $ 29.2  
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