Goodwill, Service Contracts and Other Assets - Narrative (Details) - USD ($) $ in Millions	12 Months Ended
	May 31, 2019	May 31, 2018	May 31, 2017
Finite-Lived Intangible Assets [Line Items]
Amortization of intangible assets	$ 134.0	$ 61.2	$ 22.8
Finite-Lived Intangible Assets, Net, Amortization Expense, Fiscal Year Maturity [Abstract]
Estimated amortization expense, year one	131.9
Estimated amortization expense, year two	116.9
Estimated amortization expense, year three	104.7
Estimated amortization expense, year four	86.3
Estimated amortization expense, year five	74.6
Estimated amortization expense, thereafter	$ 264.5
Capitalized contract costs
Finite-Lived Intangible Assets, Net, Amortization Expense, Fiscal Year Maturity [Abstract]
Weighted average amortization period	7 years
Noncompete and consulting agreements
Finite-Lived Intangible Assets, Net, Amortization Expense, Fiscal Year Maturity [Abstract]
Weighted average amortization period	5 years
Other
Finite-Lived Intangible Assets, Net, Amortization Expense, Fiscal Year Maturity [Abstract]
Weighted average amortization period	3 years
Service contracts
Finite-Lived Intangible Assets, Net, Amortization Expense, Fiscal Year Maturity [Abstract]
Weighted average amortization period	14 years