Business Segment Information - Segment reporting (Details) $ in Millions	12 Months Ended
	May 31, 2022 USD ($) segment	May 31, 2021 USD ($)	May 31, 2020 USD ($)
Business Segment Information
Number of business segments | segment	2
Net sales	$ 1,820.0	$ 1,652.3	$ 2,072.0
Gross profit	313.2	275.9	269.2
Total assets	1,573.9	1,539.7
Depreciation and amortization, including amortization of stock-based compensation, Net	41.3	45.5	51.0
Continuing operations
Business Segment Information
Capital expenditures	17.3	11.3	23.6
Aviation Services
Business Segment Information
Net sales	1,745.8	1,553.7	1,964.2
Gross profit	297.5	263.2	267.3
Total assets	1,367.3	1,357.2
Aviation Services | Continuing operations
Business Segment Information
Capital expenditures	16.2	8.1	16.9
Depreciation and amortization, including amortization of stock-based compensation, Gross	31.2	33.7	39.2
Expeditionary Services
Business Segment Information
Net sales	74.2	98.6	107.8
Gross profit	15.7	12.7	1.9
Total assets	74.8	73.0
Expeditionary Services | Continuing operations
Business Segment Information
Capital expenditures	1.0	3.1	5.4
Depreciation and amortization, including amortization of stock-based compensation, Gross	1.6	2.3	3.7
Corporate | Continuing operations
Business Segment Information
Capital expenditures	0.1	0.1	1.3
Depreciation and amortization, including amortization of stock-based compensation, Gross	8.5	9.5	$ 8.1
Corporate | Discontinued operations
Business Segment Information
Total assets	$ 131.8	$ 109.5