Goodwill, Service Contracts and Other Assets - Narrative (Details) - USD ($) $ in Millions	12 Months Ended
	May 31, 2022	May 31, 2021	May 31, 2020
Finite-Lived Intangible Assets [Line Items]
Amortization of intangible assets	$ 148.4	$ 141.9	$ 140.8
Service contracts
Finite-Lived Intangible Assets [Line Items]
Weighted average amortization period	13 years
Capitalized contract costs
Finite-Lived Intangible Assets [Line Items]
Weighted average amortization period	7 years
Noncompete and consulting agreements
Finite-Lived Intangible Assets [Line Items]
Weighted average amortization period	5 years
Other
Finite-Lived Intangible Assets [Line Items]
Weighted average amortization period	10 years