Segment Operations - Financial Information for Operating Segments (Detail) - USD ($)	3 Months Ended					9 Months Ended
	Feb. 28, 2023		Aug. 31, 2022	Feb. 28, 2022		Feb. 28, 2023		Feb. 28, 2022		May 31, 2022
Segment Reporting Information [Line Items]
Net sales	$ 1,103,322,000			$ 1,378,235,000		$ 3,687,528,000		$ 3,721,914,000
Impairment of long-lived assets			$ 312,000
Restructuring and other expense (income), net	824,000			(504,000)		(4,558,000)		(14,782,000)
Miscellaneous income (expense), net	1,327,000			393,000		(2,354,000)		2,063,000
Equity income	36,926,000			47,466,000		105,495,000		160,600,000
Adjusted EBIT	62,313,000			77,330,000		170,691,000		403,366,000
Total assets	3,497,672,000					3,497,672,000				$ 3,643,023,000
Steel Processing
Segment Reporting Information [Line Items]
Net sales	757,007,000			1,052,562,000		2,637,834,000		2,813,214,000
Impairment of long-lived assets				3,076,000		312,000		3,076,000
Restructuring and other expense (income), net	1,000			114,000		(4,204,000)		(12,199,000)
Miscellaneous income (expense), net	1,111,000			(12,000)		2,145,000		35,000
Equity income	(185,000)			4,692,000		3,491,000		22,864,000
Adjusted EBIT	7,788,000	[1]		7,116,000	[2]	25,450,000	[3]	186,734,000	[4]
Total assets	1,763,730,000					1,763,730,000				2,082,522,000
Consumer products
Segment Reporting Information [Line Items]
Net sales	162,647,000			161,692,000		505,145,000		450,268,000
Restructuring and other expense (income), net	206,000					206,000
Miscellaneous income (expense), net	(21,000)			(39,000)		(102,000)		169,000
Adjusted EBIT	17,943,000	[1]		26,674,000	[2]	52,350,000	[3]	64,813,000	[4]
Total assets	636,896,000					636,896,000				577,026,000
Building Products
Segment Reporting Information [Line Items]
Net sales	151,876,000			132,944,000		443,870,000		368,813,000
Impairment of long-lived assets	484,000					484,000
Restructuring and other expense (income), net	617,000			(35,000)		617,000		(35,000)
Miscellaneous income (expense), net	130,000			(3,000)		428,000		141,000
Equity income	37,836,000			39,978,000		116,809,000		132,865,000
Adjusted EBIT	51,472,000	[1]		49,570,000	[2]	145,431,000	[3]	153,042,000	[4]
Total assets	647,582,000					647,582,000				681,188,000
Sustainable Energy Solutions
Segment Reporting Information [Line Items]
Net sales	31,792,000			31,037,000		100,679,000		89,619,000
Restructuring and other expense (income), net								(143,000)
Miscellaneous income (expense), net	(37,000)			(38,000)		19,000		(16,000)
Adjusted EBIT	(1,440,000)	[1]		(2,801,000)	[2]	(1,690,000)	[3]	(4,561,000)	[4]
Total assets	121,689,000					121,689,000				114,084,000
Other
Segment Reporting Information [Line Items]
Restructuring and other expense (income), net				(583,000)		(1,177,000)		(2,405,000)
Separation costs	6,347,000					15,593,000
Miscellaneous income (expense), net	144,000			485,000		(4,844,000)		1,734,000
Equity income	(725,000)			2,796,000		(14,805,000)		4,871,000
Adjusted EBIT	(4,443,000)	[1]		4,039,000	[2]	(2,588,000)	[3]	5,517,000	[4]
Total assets	327,775,000					327,775,000				$ 188,203,000
Consolidated
Segment Reporting Information [Line Items]
Net sales	1,103,322,000			1,378,235,000		3,687,528,000		3,721,914,000
Impairment of long-lived assets	484,000			3,076,000		796,000		3,076,000
Restructuring and other expense (income), net	824,000			(504,000)		(4,558,000)		(14,782,000)
Separation costs	6,347,000					15,593,000
Miscellaneous income (expense), net	1,327,000			393,000		(2,354,000)		2,063,000
Equity income	36,926,000			47,466,000		105,495,000		160,600,000
Adjusted EBIT	$ 71,320,000	[1]		$ 84,598,000	[2]	$ 218,953,000	[3]	$ 405,545,000	[4]

[1] Excludes the following: • A pre-tax benefit of $1,050,000 within selling, general, and administrative expense (“SG&A”) to reverse the compensation expense accrued during the first six months of fiscal 2023 for the anticipated payout under the first annual earnout period ending December 31, 2023 associated with the Level5 acquisition (see the discussion of this acquisition in “Note P – Acquisitions”); • Separation costs of $6,347,000 within Other related to direct and incremental costs incurred in connection with the anticipated Separation, including audit, advisory, and legal costs; and • A loss of $300,000 for the settlement of final transaction costs within Other related to the sale of our 50% noncontrolling equity investment in ArtiFlex.

[2] Excludes the noncontrolling interest portion of the impairment of long-lived assets and restructuring expense within Steel Processing of $1,139,000.

[3] Excludes the noncontrolling interest portion of the impairment of long-lived assets and restructuring income within Steel Processing of $1,734,000.

[4] Excludes the noncontrolling interest portion of impairment of long-lived assets and restructuring income within Steel Processing of $4,888,000.