Business Segment Information - Segment reporting (Details) $ in Millions	12 Months Ended
	May 31, 2023 USD ($) segment	May 31, 2022 USD ($)	May 31, 2021 USD ($)
Business Segment Information
Number of business segments | segment	2
Net sales	$ 1,990.5	$ 1,820.0	$ 1,652.3
Gross profit	370.1	313.2	275.9
Total assets	1,833.1	1,573.9
Depreciation and amortization, including amortization of stock-based compensation, Net	$ 41.4	41.3	45.5
Number of new operating segments from separation of a segment | segment	3
Number of operating segments | segment	4
Continuing operations
Business Segment Information
Capital expenditures	$ 29.5	17.3	11.3
Aviation Services
Business Segment Information
Net sales	1,898.7	1,745.8	1,553.7
Gross profit	355.1	297.5	263.2
Total assets	1,617.1	1,367.3
Aviation Services | Continuing operations
Business Segment Information
Capital expenditures	23.0	16.2	8.1
Depreciation and amortization, including amortization of stock-based compensation, Gross	25.7	31.2	33.7
Expeditionary Services
Business Segment Information
Net sales	91.8	74.2	98.6
Gross profit	15.0	15.7	12.7
Total assets	67.0	74.8
Expeditionary Services | Continuing operations
Business Segment Information
Capital expenditures	6.1	1.0	3.1
Depreciation and amortization, including amortization of stock-based compensation, Gross	1.5	1.6	2.3
Corporate | Continuing operations
Business Segment Information
Capital expenditures	0.4	0.1	0.1
Depreciation and amortization, including amortization of stock-based compensation, Gross	14.2	8.5	$ 9.5
Corporate | Discontinued operations
Business Segment Information
Total assets	$ 149.0	$ 131.8