Segment Operations - Financial Information for Reportable Segments (Detail) - USD ($)	3 Months Ended					6 Months Ended
	Nov. 30, 2022		Aug. 31, 2022	Nov. 30, 2021		Nov. 30, 2022		Nov. 30, 2021		May 31, 2022
Segment Reporting Information [Line Items]
Net sales	$ 1,175,541,000			$ 1,232,861,000		$ 2,584,206,000		$ 2,343,679,000
Impairment of long-lived assets	0		$ 312,000					0
Restructuring and other income, net	(4,282,000)			(2,004,000)		(5,382,000)		(14,278,000)
Miscellaneous income (expense), net	1,405,000			1,040,000		(3,681,000)		1,670,000
Equity in net income (loss) of unconsolidated affiliates	36,857,000			60,218,000		68,569,000		113,134,000
Adjusted EBIT	23,636,000			144,411,000		108,378,000		326,036,000
Total assets	3,390,660,000					3,390,660,000				$ 3,643,023,000
Steel Processing
Segment Reporting Information [Line Items]
Net sales	841,947,000			937,842,000		1,880,827,000		1,760,652,000
Impairment of long-lived assets						312,000
Restructuring and other income, net	(4,282,000)			(182,000)		(4,205,000)		(12,313,000)
Miscellaneous income (expense), net	850,000			17,000		1,035,000		47,000
Equity in net income (loss) of unconsolidated affiliates	1,906,000			8,823,000		3,676,000		18,172,000
Adjusted EBIT	(17,249,000)	[1],[2]		71,925,000	[3]	17,663,000	[4],[5]	179,617,000	[6]
Total assets	1,796,136,000					1,796,136,000				2,082,522,000
Consumer products
Segment Reporting Information [Line Items]
Net sales	153,795,000			140,793,000		342,497,000		288,576,000
Miscellaneous income (expense), net	(47,000)			159,000		(82,000)		209,000
Adjusted EBIT	13,473,000	[1],[2]		17,584,000	[3]	34,406,000	[4],[5]	38,140,000	[6]
Total assets	627,474,000					627,474,000				577,026,000
Building Products
Segment Reporting Information [Line Items]
Net sales	141,671,000			121,125,000		291,994,000		235,868,000
Miscellaneous income (expense), net	76,000			218,000		299,000		144,000
Equity in net income (loss) of unconsolidated affiliates	35,107,000			49,894,000		78,973,000		92,887,000
Adjusted EBIT	41,224,000	[1],[2]		54,718,000	[3]	93,959,000	[4],[5]	103,471,000	[6]
Total assets	645,566,000					645,566,000				681,188,000
Sustainable Energy Solutions
Segment Reporting Information [Line Items]
Net sales	38,128,000			33,101,000		68,888,000		58,583,000
Restructuring and other income, net								(143,000)
Miscellaneous income (expense), net	142,000			82,000		56,000		22,000
Adjusted EBIT	1,143,000	[1],[2]		796,000	[3]	(250,000)	[4],[5]	(1,760,000)	[6]
Total assets	120,978,000					120,978,000				114,084,000
Other
Segment Reporting Information [Line Items]
Restructuring and other income, net				(1,822,000)		(1,177,000)		(1,822,000)
Separation costs	9,246,000					9,246,000
Miscellaneous income (expense), net	384,000			564,000		(4,989,000)		1,248,000
Equity in net income (loss) of unconsolidated affiliates	(156,000)			1,501,000		(14,080,000)		2,075,000
Adjusted EBIT	(3,291,000)	[1],[2]		1,893,000	[3]	1,854,000	[4],[5]	1,479,000	[6]
Total assets	200,506,000					200,506,000				$ 188,203,000
Consolidated
Segment Reporting Information [Line Items]
Net sales	1,175,541,000			1,232,861,000		2,584,206,000		2,343,679,000
Impairment of long-lived assets						312,000
Restructuring and other income, net	(4,282,000)			(2,004,000)		(5,382,000)		(14,278,000)
Separation costs	9,246,000					9,246,000
Miscellaneous income (expense), net	1,405,000			1,040,000		(3,681,000)		1,670,000
Equity in net income (loss) of unconsolidated affiliates	36,857,000			60,218,000		68,569,000		113,134,000
Adjusted EBIT	$ 35,300,000	[1],[2]		$ 146,916,000	[3]	$ 147,632,000	[4],[5]	$ 320,947,000	[6]

[1] Excludes $525 in selling, general and administrative expense in Consumer Products related to incremental expense attributable to the Level5 earnout; excludes $9,246 of Separation costs in Other related to direct and incremental costs incurred in connection with the anticipated Separation, including audit, advisory, and legal costs.

[2] Excludes the noncontrolling interest portion of the restructuring gains within Steel Processing of $1,850.

[3] Excludes the noncontrolling interest portion of the restructuring gains within Steel Processing of $81.

[4] Excludes a non-cash settlement charge of $4,774 in miscellaneous income (expense), net within Other to accelerate a portion of deferred pension cost as a result of a pension lift-out transaction executed with a third-party insurance company to transfer a portion of the total projected benefit obligation of The Gerstenslager Company Bargaining Unit Employees’ Pension Plan to the third-party insurance company; excludes a loss of $15,759 in equity in net income (loss) of unconsolidated affiliates within Other related to the sale of the Company’s 50% noncontrolling equity investment in ArtiFlex effective August 3, 2022; excludes $1,050 in selling, general and administrative expense in Consumer Products related to incremental compensation expense attributable to the Level5 earnout; and excludes $9,246 of Separation costs in Other related to direct and incremental costs incurred in connection with the anticipated Separation, including audit, advisory, and legal costs.

[5] Excludes the noncontrolling interest portion of the impairment charge and restructuring gains within Steel Processing of $1,734.

[6] Excludes the noncontrolling interest portion of the restructuring gains within Steel Processing of $6,027.