Business Segment Information - Sales and Gross Profit (Details) $ in Millions	3 Months Ended		9 Months Ended
	Feb. 28, 2023 USD ($)	Feb. 28, 2022 USD ($)	Feb. 28, 2023 USD ($) segment	Feb. 28, 2022 USD ($)
Disaggregation of revenue by major customer markets
Operating segments | segment			2
Net sales	$ 521.1	$ 452.2	$ 1,437.2	$ 1,343.9
Gross profit	94.3	80.4	262.0	223.4
Aviation Services
Disaggregation of revenue by major customer markets
Net sales	499.1	438.0	1,368.8	1,292.9
Gross profit	90.7	77.9	251.0	212.8
Expeditionary Services
Disaggregation of revenue by major customer markets
Net sales	22.0	14.2	68.4	51.0
Gross profit	$ 3.6	$ 2.5	$ 11.0	$ 10.6