Description of Business, Basis of Presentation, and Significant Accounting Policies (Narrative) (Details) $ in Millions	3 Months Ended		9 Months Ended		12 Months Ended
	Feb. 28, 2022 USD ($) Item	Feb. 28, 2021 USD ($) Item	Feb. 28, 2022 USD ($) Segment Item	Feb. 28, 2021 USD ($) Item	May 31, 2022 USD ($)	May 31, 2021 USD ($) Item
Accounting Policies [Line Items]
Number of reportable segments | Segment			1
Allowance for credit losses	$ 17.8		$ 17.8			$ 16.0
Advance collections	1.6		1.6			2.5
Maximum individual health insurance claims liability						0.3
Stock-based compensation costs recognized	$ 12.8	$ 12.6	$ 39.2	$ 38.1
ASU No. 2020-08 [Member]
Accounting Policies [Line Items]
Change in accounting principle, accounting standards update, adoption date	Jun. 01, 2021		Jun. 01, 2021
Change in accounting principle, accounting standards update, adopted [true false]	true		true
Change in accounting principle, accounting standards update, immaterial effect [true false]	true		true
ASU No. 2019-12 [Member]
Accounting Policies [Line Items]
Change in accounting principle, accounting standards update, adoption date	Jun. 01, 2021		Jun. 01, 2021
Change in accounting principle, accounting standards update, adopted [true false]	true		true
Change in accounting principle, accounting standards update, immaterial effect [true false]	true		true
Forecast [Member]
Accounting Policies [Line Items]
Maximum individual health insurance claims liability					$ 0.5
Trade Receivables [Member]
Accounting Policies [Line Items]
Receivables	$ 120.2		$ 120.2			98.4
Purchased Receivables [Member]
Accounting Policies [Line Items]
Receivables	$ 618.5		$ 618.5			$ 495.9
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	0	0
PEO [Member]
Accounting Policies [Line Items]
Maximum 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] | Forecast [Member]
Accounting Policies [Line Items]
Individual workers' compensation claims liability					1.0
PEO Aggregate Claims Exceeding $1.0M [Member] | Maximum [Member] | Forecast [Member]
Accounting Policies [Line Items]
Maximum individual workers' compensation claims liability					$ 2.0