Goodwill and Intangible Assets - Intangible Assets (Details) - USD ($) $ in Thousands	Feb. 28, 2023	May 31, 2022
Finite-Lived Intangible Assets [Line Items]
Gross carrying value, finite intangible items	$ 309,175	$ 314,369
Accumulated amortization	(175,164)	(161,989)
Net carrying value, finite intangible items	134,011	152,380
Product technologies
Finite-Lived Intangible Assets [Line Items]
Gross carrying value, finite intangible items	233,752	239,467
Accumulated amortization	(122,017)	(112,141)
Net carrying value, finite intangible items	111,735	127,326
Customer relationships
Finite-Lived Intangible Assets [Line Items]
Gross carrying value, finite intangible items	60,096	60,115
Accumulated amortization	(40,995)	(38,003)
Net carrying value, finite intangible items	19,101	22,112
Trademarks
Finite-Lived Intangible Assets [Line Items]
Gross carrying value, finite intangible items	9,950	9,950
Accumulated amortization	(7,396)	(7,185)
Net carrying value, finite intangible items	2,554	2,765
Licenses
Finite-Lived Intangible Assets [Line Items]
Gross carrying value, finite intangible items	5,377	4,837
Accumulated amortization	(4,756)	(4,660)
Net carrying value, finite intangible items	$ 621	$ 177