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Goodwill and Intangible Assets - Intangible Assets (Details) - USD ($) $ in Thousands | Aug. 31, 2023 | May 31, 2023
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Finite-Lived Intangible Assets [Line Items] |  |
Gross carrying value, finite intangible items | $ 280,404 | $ 281,547
Accumulated amortization | (173,733) | (170,403)
Net carrying value, finite intangible items | 106,671 | 111,144
Product technologies |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross carrying value, finite intangible items | 210,589 | 211,751
Accumulated amortization | (120,652) | (118,314)
Net carrying value, finite intangible items | 89,937 | 93,437
Customer relationships |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross carrying value, finite intangible items | 57,528 | 57,509
Accumulated amortization | (41,714) | (40,755)
Net carrying value, finite intangible items | 15,814 | 16,754
Trademarks |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross carrying value, finite intangible items | 7,450 | 7,450
Accumulated amortization | (6,689) | (6,660)
Net carrying value, finite intangible items | 761 | 790
Licenses |  |
Finite-Lived Intangible Assets [Line Items] |  |
Gross carrying value, finite intangible items | 4,837 | 4,837
Accumulated amortization | (4,678) | (4,674)
Net carrying value, finite intangible items | $ 159 | $ 163

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