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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 |  |  |

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