Revenue Recognition - Disaggregation of Revenue (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Nov. 30, 2024	Nov. 30, 2023	Nov. 30, 2024	Nov. 30, 2023
Disaggregation of revenue by major customer markets
Net sales	$ 686.1	$ 545.4	$ 1,347.8	$ 1,095.1
Parts Supply
Disaggregation of revenue by major customer markets
Net sales	273.7	227.6	523.4	464.4
Parts Supply | Commercial
Disaggregation of revenue by major customer markets
Net sales	220.8	189.4	431.2	395.4
Parts Supply | Government and defense
Disaggregation of revenue by major customer markets
Net sales	52.9	38.2	92.2	69.0
Repair & Engineering
Disaggregation of revenue by major customer markets
Net sales	228.8	145.4	446.4	282.9
Repair & Engineering | Commercial
Disaggregation of revenue by major customer markets
Net sales	206.7	130.9	397.9	252.5
Repair & Engineering | Government and defense
Disaggregation of revenue by major customer markets
Net sales	22.1	14.5	48.5	30.4
Integrated Solutions
Disaggregation of revenue by major customer markets
Net sales	163.4	156.6	332.3	312.9
Integrated Solutions | Commercial
Disaggregation of revenue by major customer markets
Net sales	72.0	63.4	142.0	126.2
Integrated Solutions | Government and defense
Disaggregation of revenue by major customer markets
Net sales	91.4	93.2	190.3	186.7
Aviation Services
Disaggregation of revenue by major customer markets
Net sales	686.1	545.4	1,347.8	1,095.1
Aviation Services | U.S./Canada
Disaggregation of revenue by major customer markets
Net sales	500.4	405.4	973.8	814.3
Aviation Services | Europe/Africa
Disaggregation of revenue by major customer markets
Net sales	108.8	81.8	217.6	173.2
Aviation Services | Asia/South Pacific
Disaggregation of revenue by major customer markets
Net sales	65.6	44.9	129.6	86.1
Aviation Services | Other
Disaggregation of revenue by major customer markets
Net sales	11.3	13.3	26.8	21.5
Expeditionary Services
Disaggregation of revenue by major customer markets
Net sales	20.2	15.8	45.7	34.9
Expeditionary Services | Commercial
Disaggregation of revenue by major customer markets
Net sales	0.7	1.5	2.0	3.6
Expeditionary Services | Government and defense
Disaggregation of revenue by major customer markets
Net sales	$ 19.5	$ 14.3	$ 43.7	$ 31.3