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Goodwill, Service Contracts and Other Assets - Narrative (Details) - USD ($)
$ in Millions
3 Months Ended 6 Months Ended
Nov. 30, 2018
Nov. 30, 2017
Nov. 30, 2018
Nov. 30, 2017
Goodwill, Service Contracts and Other Assets [Abstract]        
Amortization expense for service contracts and other assets $ 33.3 $ 15.6 $ 66.2 $ 29.8
Estimated amortization expense, year one 132.6   132.6  
Estimated amortization expense, year two 124.7   124.7  
Estimated amortization expense, year three 109.6   109.6  
Estimated amortization expense, year four 97.7   97.7  
Estimated amortization expense, year five 79.7   79.7  
Estimated amortization expense, thereafter $ 323.1   $ 323.1