Description of Business, Basis of Presentation, and Significant Accounting Policies (Narrative) (Details) $ in Millions	3 Months Ended		12 Months Ended
	Aug. 31, 2022 USD ($) Item Segment	Aug. 31, 2021 USD ($) Item	May 31, 2023 USD ($)	May 31, 2022 USD ($) Item
Accounting Policies [Line Items]
Number of reportable segments | Segment	1
Allowance for credit losses	$ 19.8			$ 18.2
Advance collections	12.4			2.6
Maximum individual health insurance claims liability				0.5
Stock-based compensation costs recognized	$ 14.4	$ 12.4
Accounting Standards Update 2021-10 [Member]
Accounting Policies [Line Items]
Change in accounting principle, accounting standards update, adoption date	Jun. 01, 2022
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	$ 300.2			123.2
Purchased Receivables [Member]
Accounting Policies [Line Items]
Receivables	$ 596.0			$ 618.8
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 [Member]
Accounting Policies [Line Items]
Individual workers' compensation claims liability				$ 1.0
PEO [Member] | Forecast [Member]
Accounting Policies [Line Items]
Individual workers' compensation claims liability			1.0
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			$ 2.0