Business Segment Information - Significant expenses for each segment (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Feb. 28, 2026	Feb. 28, 2025	Feb. 28, 2026	Feb. 28, 2025
Business Segment Information
Number of reportable segments not disclosed			true
Sales	$ 845.1	$ 678.2	$ 2,380.0	$ 2,026.0
Cost of Sales	690.4	546.5	1,934.7	1,648.5
Selling, General and Administrative	89.8	61.3	249.7	270.3
Operating Income	65.8	71.1	197.7	112.2
Bargain purchase gain	35.7		35.7
Gain on sale of headquarters building	9.8		9.8
Gain (loss) related to sale and exit of businesses, net	(0.4)	(64.0)	0.2	(65.3)
Other expense, net	(0.7)	(0.1)	(1.0)	(0.4)
Interest expense	(17.5)	(18.5)	(55.4)	(56.6)
Interest income	0.4	0.4	1.2	1.4
Income (loss) before income taxes	93.1	(11.1)	188.2	(8.7)
Inter-segment Sales
Business Segment Information
Sales	28.2	28.3	86.0	77.9
Total Sales
Business Segment Information
Sales	873.3	706.5	2,466.0	2,103.9
Reportable segment, aggregation before corporate and other operating segment
Business Segment Information
Sales	845.1	678.2	2,380.0	2,026.0
Cost of Sales	690.2	545.8	1,934.8	1,646.8
Selling, General and Administrative	78.3	52.7	217.3	183.5
Other Segment Items	(1.4)	(0.7)	(4.0)	(5.0)
Operating Income	78.0	80.4	231.9	200.7
Parts Supply
Business Segment Information
Sales	392.5	270.7	1,063.9	794.1
Cost of Sales	311.4	215.9	851.6	635.0
Selling, General and Administrative	31.7	10.1	84.7	53.1
Other Segment Items	(1.3)	(0.7)	(4.9)	(1.1)
Operating Income	50.7	45.4	132.5	107.1
Parts Supply | Inter-segment Sales
Business Segment Information
Sales	8.0	7.3	23.4	12.5
Parts Supply | Total Sales
Business Segment Information
Sales	400.5	278.0	1,087.3	806.6
Repair & Engineering
Business Segment Information
Sales	265.3	215.9	724.4	662.3
Cost of Sales	222.9	173.3	589.8	528.6
Selling, General and Administrative	27.4	23.4	75.2	74.1
Other Segment Items	(0.1)	0.2	1.2	(3.3)
Operating Income	15.1	19.0	58.2	62.9
Repair & Engineering | Inter-segment Sales
Business Segment Information
Sales	17.7	20.5	56.2	64.3
Repair & Engineering | Total Sales
Business Segment Information
Sales	283.0	236.4	780.6	726.6
Integrated Solutions
Business Segment Information
Sales	167.8	162.9	528.6	495.2
Cost of Sales	140.8	136.2	443.5	420.8
Selling, General and Administrative	17.7	17.3	52.4	51.2
Other Segment Items	(0.1)	(0.2)	(0.3)	(0.6)
Operating Income	9.4	9.6	33.0	23.8
Integrated Solutions | Inter-segment Sales
Business Segment Information
Sales	2.5	0.5	6.4	1.1
Integrated Solutions | Total Sales
Business Segment Information
Sales	170.3	163.4	535.0	496.3
Expeditionary Services
Business Segment Information
Sales	19.5	28.7	63.1	74.4
Cost of Sales	15.1	20.4	49.9	62.4
Selling, General and Administrative	1.5	1.9	5.0	5.1
Other Segment Items	0.1
Operating Income	2.8	6.4	8.2	6.9
Expeditionary Services | Total Sales
Business Segment Information
Sales	19.5	28.7	63.1	74.4
Corporate and other
Business Segment Information
Operating Income	$ (12.2)	$ (9.3)	$ (34.2)	$ (88.5)