Business Segment Information - Sales and Gross Profit (Details) - USD ($) $ in Millions	12 Months Ended
	May 31, 2024	May 31, 2023	May 31, 2022
Business Segment Information
Total assets	$ 2,770.0	$ 1,833.1
Continuing operations
Business Segment Information
Capital expenditures	29.7	29.5	$ 17.3
Depreciation and amortization, including amortization of stock-based compensation, Gross	56.5	41.4	41.3
Continuing operations | Corporate
Business Segment Information
Depreciation and amortization, including amortization of stock-based compensation, Gross	17.0	14.2	8.5
Discontinued operations | Corporate
Business Segment Information
Total assets	180.6	161.7
Parts Supply
Business Segment Information
Total assets	732.8	587.6
Parts Supply | Continuing operations
Business Segment Information
Capital expenditures	0.8	2.2	2.0
Depreciation and amortization, including amortization of stock-based compensation, Gross	8.4	6.2	6.8
Repair & Engineering
Business Segment Information
Total assets	1,235.4	433.4
Repair & Engineering | Continuing operations
Business Segment Information
Capital expenditures	11.9	15.1	12.8
Depreciation and amortization, including amortization of stock-based compensation, Gross	12.2	7.6	8.8
Integrated Solutions
Business Segment Information
Total assets	542.1	583.4
Integrated Solutions | Continuing operations
Business Segment Information
Capital expenditures	5.2	5.7	1.4
Depreciation and amortization, including amortization of stock-based compensation, Gross	17.4	11.9	15.6
Expeditionary Services
Business Segment Information
Total assets	79.1	67.0
Expeditionary Services | Continuing operations
Business Segment Information
Capital expenditures	8.5	6.1	1.0
Depreciation and amortization, including amortization of stock-based compensation, Gross	1.5	1.5	1.6
Corporate and other | Continuing operations
Business Segment Information
Capital expenditures	$ 3.3	$ 0.4	$ 0.1