Restructuring and Other Income, Net - Schedule of Progression of Liabilities Associated with Restructuring Activities, Combined with Reconciliation to Restructuring and Other Income, Net (Detail) - USD ($) $ in Thousands		3 Months Ended		9 Months Ended
		Feb. 28, 2022	Feb. 28, 2021	Feb. 28, 2022	Feb. 28, 2021
Restructuring Cost and Reserve [Line Items]
Beginning Balance				$ 1,220
Expense (income)				(685)
Payments				(164)
Adjustments				(58)
Ending Balance		$ 313		313
Net gain on sale of assets	[1],[2]			(13,240)
Gain on lease buyout	[3]			(857)
Restructuring and other income, net		(504)	$ 28,212	(14,782)	$ 37,656
Early Retirement And Severance
Restructuring Cost and Reserve [Line Items]
Beginning Balance				771
Expense (income)				(236)
Payments				(164)
Adjustments				(58)
Ending Balance		313		313
Facility Exit And Other Costs
Restructuring Cost and Reserve [Line Items]
Beginning Balance				449
Expense (income)				(449)
Payments				0
Adjustments				0
Ending Balance		$ 0		$ 0

[1] On June 9, 2021, the Company’s consolidated joint venture, WSP, sold the remaining assets of its Canton, Michigan, facility for net cash proceeds of $19,850,000, resulting in a pre-tax gain of $12,244,000.  Net assets previously classified as held for sale were $7,606,000.

[2] During the current fiscal year, the Company sold real property in Wooster and Bremen, Ohio, for net cash proceeds of $8,723,000, resulting in pre-tax gains of $860,000. These assets were excluded from the sale of the Company’s former oil & gas equipment business in January 2021. The combined net book value classified as assets held for sale immediately prior to closing was $7,863,000.

[3] On September 10, 2021, the Company executed an agreement to buy out the remaining term of the operating lease at its fabricated products business in Stow, Ohio, for $1,100,000, resulting in a pre-tax gain of $857,000.  This facility was retained in connection with the divestiture of the Company’s former engineered cabs business and had not been operational since June 2020.