Goodwill and Intangible Assets - Intangible Assets (Details) - USD ($) $ in Thousands	Feb. 28, 2022	May 31, 2021
Finite-Lived Intangible Assets [Line Items]
Gross carrying value, finite intangible items	$ 316,678	$ 313,235
Accumulated amortization	(157,573)	(144,258)
Net carrying value, finite intangible items	159,105	168,977
Product technologies
Finite-Lived Intangible Assets [Line Items]
Gross carrying value, finite intangible items	241,719	236,907
Accumulated amortization	(108,757)	(97,343)
Net carrying value, finite intangible items	132,962	139,564
Customer relationships
Finite-Lived Intangible Assets [Line Items]
Gross carrying value, finite intangible items	60,172	60,291
Accumulated amortization	(37,057)	(34,164)
Net carrying value, finite intangible items	23,115	26,127
Trademarks
Finite-Lived Intangible Assets [Line Items]
Gross carrying value, finite intangible items	9,950	9,950
Accumulated amortization	(7,115)	(6,905)
Net carrying value, finite intangible items	2,835	3,045
Licenses
Finite-Lived Intangible Assets [Line Items]
Gross carrying value, finite intangible items	4,837	6,087
Accumulated amortization	(4,644)	(5,846)
Net carrying value, finite intangible items	$ 193	$ 241