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Description of Business, Basis of Presentation, and Significant Accounting Policies (Narrative) (Details) $ / shares in Units, $ in Millions |  |  | 12 Months Ended
--- | --- | --- | ---
Jul. 08, 2021 $ / shares | Jul. 07, 2021 USD ($) | May 31, 2021 USD ($) segment | May 31, 2020 USD ($) | May 31, 2019 USD ($)
Accounting Policies [Line Items] |  |  |  |  |
Number of reportable segments | segment |  |  | 1 |  |
Cash and cash equivalents |  |  | $ 995.2 | $ 905.2 | $ 673.6
Allowance for doubtful accounts |  |  | 16.0 | 12.5 |
Advance collections |  |  | 2.5 | 6.1 |
Goodwill |  |  | 1,820.7 | 1,791.1 | 1,782.6
Goodwill, impairment loss |  |  | 0.0 | 0.0 | 0.0
Impairment of intangible assets with indefinite useful lives |  |  | 0.0 | 0.0 | 0.0
Impairment of long-lived assets |  |  | 0.0 | 0.0 | 0.0
Realized gains or losses from foreign exchange transactions |  |  | 0.0 | 0.0 | 0.0
Impairment loss, assets recognized from the costs to obtain and fufill contracts |  |  | 0.0 | 0.0 | $ 0.0
Workers' compensation insurance costs in current liabilities |  |  | 65.3 | 72.3 |
Workers' compensation insurance costs in long-term liabilities |  |  | 117.8 | 101.3 |
Maximum individual health insurance claims liability |  |  | 0.3 | 0.3 |
PEO accrued health insurance and dental and vision plan reserves in current liabilities |  |  | 43.9 | 36.7 |
Operating lease, impairment loss |  |  | 0.0 | 0.0 |
Subsequent Event [Member] |  |  |  |  |
Accounting Policies [Line Items] |  |  |  |  |
Authorization repurchase expiration date |  | Jan. 31, 2024 |  |  |
Declared date | Jul. 08, 2021 |  |  |  |
Quarterly dividend per share | $ / shares | $ 0.66 |  |  |  |
Payable date | Aug. 26, 2021 |  |  |  |
Record date | Aug. 02, 2021 |  |  |  |
Trade Receivables [Member] |  |  |  |  |
Accounting Policies [Line Items] |  |  |  |  |
Receivables |  |  | 98.4 | 84.7 |
Purchased Receivables [Member] |  |  |  |  |
Accounting Policies [Line Items] |  |  |  |  |
Receivables |  |  | $ 495.9 | $ 311.9 |
Minimum [Member] |  |  |  |  |
Accounting Policies [Line Items] |  |  |  |  |
Payroll funding fees average collection period |  |  | 35 days |  |
Minimum [Member] | Finite Lived Assets [Member] |  |  |  |  |
Accounting Policies [Line Items] |  |  |  |  |
Amortization period |  |  | 3 years |  |
Minimum [Member] | Software [Member] |  |  |  |  |
Accounting Policies [Line Items] |  |  |  |  |
Estimated useful lives |  |  | 3 years |  |
Minimum [Member] | Software Development [Member] |  |  |  |  |
Accounting Policies [Line Items] |  |  |  |  |
Estimated useful lives |  |  | 12 years |  |
Maximum [Member] |  |  |  |  |
Accounting Policies [Line Items] |  |  |  |  |
Payroll funding fees average collection period |  |  | 45 days |  |
Maximum [Member] | Subsequent Event [Member] |  |  |  |  |
Accounting Policies [Line Items] |  |  |  |  |
Amount authorize to repurchase |  | $ 400.0 |  |  |
Maximum [Member] | Finite Lived Assets [Member] |  |  |  |  |
Accounting Policies [Line Items] |  |  |  |  |
Amortization period |  |  | 12 years |  |
Maximum [Member] | Software [Member] |  |  |  |  |
Accounting Policies [Line Items] |  |  |  |  |
Estimated useful lives |  |  | 5 years |  |
Europe [Member] | Revenue [Member] | Geographic Concentration Risk [Member] |  |  |  |  |
Accounting Policies [Line Items] |  |  |  |  |
Concentration percentage |  |  | 1.00% | 1.00% | 1.00%
Europe [Member] | Long Lived Assets [Member] | Geographic Concentration Risk [Member] |  |  |  |  |
Accounting Policies [Line Items] |  |  |  |  |
Concentration percentage |  |  | 7.00% | 5.00% |
PEO And Insurance Solutions [Member] |  |  |  |  |
Accounting Policies [Line Items] |  |  |  |  |
Cash and cash equivalents |  |  | $ 150.5 | $ 136.4 |
PEO [Member] |  |  |  |  |
Accounting Policies [Line Items] |  |  |  |  |
Maximum individual workers' compensation claims liability |  |  | $ 1.0 | $ 1.0 |

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