Fair Value Measurements - Assets Measured at Fair Value on Non-Recurring Basis (Parenthetical) (Detail) - USD ($)	12 Months Ended
	May 31, 2022	May 31, 2021	May 31, 2020	Aug. 31, 2020
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Impairment of goodwill and long-lived assets	$ 3,076,000	$ 13,739,000	$ 82,690,000
Fair Value, Nonrecurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets Fair Value Disclosure	700,000	400,000
TWB Hermosillo
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Impairment of ROU assets			565,000
Packing Solutions Business
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Impairment of goodwill and long-lived assets			2,544,000
Long Lived Assets Held And Used
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets Fair Value Disclosure			2,800,000
Long Lived Assets Held And Used | Engineered Cabs | Fair Value, Nonrecurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets Fair Value Disclosure				$ 12,860,000
Long Lived Assets Held And Used | Packing Solutions Business
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Carrying value long-lived assets			2,810,000
Long Lived Assets Held And Used | Packing Solutions Business | Fair Value, Nonrecurring
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets Fair Value Disclosure			$ 266,000
Long Lived Assets Held And Used | Jefferson
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets Fair Value Disclosure		$ 400,000,000
Long Lived Assets Held And Used | Production Equipment Member | Twinsburg Member
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Assets Fair Value Disclosure	$ 700,000,000