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Goodwill and Intangible Assets - Intangible Assets (Details) - USD ($)
$ in Thousands
Nov. 30, 2022
May 31, 2022
Finite-Lived Intangible Assets [Line Items]    
Gross carrying value, finite intangible items $ 313,266 $ 314,369
Accumulated amortization (171,323) (161,989)
Net carrying value, finite intangible items 141,943 152,380
Product technologies    
Finite-Lived Intangible Assets [Line Items]    
Gross carrying value, finite intangible items 237,863 239,467
Accumulated amortization (119,301) (112,141)
Net carrying value, finite intangible items 118,562 127,326
Customer relationships    
Finite-Lived Intangible Assets [Line Items]    
Gross carrying value, finite intangible items 60,076 60,115
Accumulated amortization (39,972) (38,003)
Net carrying value, finite intangible items 20,104 22,112
Trademarks    
Finite-Lived Intangible Assets [Line Items]    
Gross carrying value, finite intangible items 9,950 9,950
Accumulated amortization (7,326) (7,185)
Net carrying value, finite intangible items 2,624 2,765
Licenses    
Finite-Lived Intangible Assets [Line Items]    
Gross carrying value, finite intangible items 5,377 4,837
Accumulated amortization (4,724) (4,660)
Net carrying value, finite intangible items $ 653 $ 177