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Description of Business, Basis of Presentation, and Significant Accounting Policies (Narrative) (Details) $ in Millions | 3 Months Ended | 12 Months Ended
--- | --- | ---
Aug. 31, 2023 USD ($) Item Segment | Aug. 31, 2022 USD ($) Item | May 31, 2024 USD ($) | May 31, 2023 USD ($) Item
Accounting Policies [Line Items] |  |  |  |
Number of reportable segments | Segment | 1 |  |  |
Allowance for credit losses | $ 20.8 |  |  | $ 20.5
Advance collections | 28.2 |  |  | 12.5
Maximum individual health insurance claims liability |  |  |  | 0.5
Stock-based compensation costs recognized | $ 16.0 | $ 14.4 |  |
Accounting Standards Update 2021-08 [Member] |  |  |  |
Accounting Policies [Line Items] |  |  |  |
Change in accounting principle, accounting standards update, adoption date | Jun. 01, 2023 |  |  |
Change in accounting principle, accounting standards update, adopted [true false] | true |  |  |
Change in accounting principle, accounting standards update, immaterial effect [true false] | true |  |  |
Forecast [Member] |  |  |  |
Accounting Policies [Line Items] |  |  |  |
Maximum individual health insurance claims liability |  |  | $ 0.5 |
Trade Receivables [Member] |  |  |  |
Accounting Policies [Line Items] |  |  |  |
Receivables | $ 200.8 |  |  | 287.0
Purchased Receivables [Member] |  |  |  |
Accounting Policies [Line Items] |  |  |  |
Receivables | $ 835.8 |  |  | $ 606.8
Accounts And Unbilled Receivables [Member] |  |  |  |
Accounting Policies [Line Items] |  |  |  |
Number of clients creating a credit concentration | Item | 0 |  |  | 0
Revenue [Member] |  |  |  |
Accounting Policies [Line Items] |  |  |  |
Number of clients creating a credit concentration | Item | 0 | 0 |  |
PEO Aggregate Claims Exceeding $1.0M [Member] | Minimum [Member] |  |  |  |
Accounting Policies [Line Items] |  |  |  |
Individual workers' compensation claims liability |  |  |  | $ 1.0
PEO Aggregate Claims Exceeding $1.0M [Member] | Minimum [Member] | Forecast [Member] |  |  |  |
Accounting Policies [Line Items] |  |  |  |
Individual workers' compensation claims liability |  |  | 1.0 |
PEO Aggregate Claims Exceeding $1.0M [Member] | Maximum [Member] |  |  |  |
Accounting Policies [Line Items] |  |  |  |
Maximum individual workers' compensation claims liability |  |  |  | $ 2.0
PEO Aggregate Claims Exceeding $1.0M [Member] | Maximum [Member] | Forecast [Member] |  |  |  |
Accounting Policies [Line Items] |  |  |  |
Maximum individual workers' compensation claims liability |  |  | $ 1.0 |

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