Revenue Recognition - Disaggregation of Revenue (Details) - USD ($) $ in Millions	3 Months Ended
	Aug. 31, 2024	Aug. 31, 2023
Disaggregation of revenue by major customer markets
Net sales	$ 661.7	$ 549.7
Parts Supply
Disaggregation of revenue by major customer markets
Net sales	249.7	236.8
Parts Supply | Commercial
Disaggregation of revenue by major customer markets
Net sales	210.4	206.0
Parts Supply | Government and defense
Disaggregation of revenue by major customer markets
Net sales	39.3	30.8
Repair & Engineering
Disaggregation of revenue by major customer markets
Net sales	217.6	137.5
Repair & Engineering | Commercial
Disaggregation of revenue by major customer markets
Net sales	191.2	121.6
Repair & Engineering | Government and defense
Disaggregation of revenue by major customer markets
Net sales	26.4	15.9
Integrated Solutions
Disaggregation of revenue by major customer markets
Net sales	168.9	156.3
Integrated Solutions | Commercial
Disaggregation of revenue by major customer markets
Net sales	70.0	62.8
Integrated Solutions | Government and defense
Disaggregation of revenue by major customer markets
Net sales	98.9	93.5
Aviation Services
Disaggregation of revenue by major customer markets
Net sales	661.7	549.7
Aviation Services | U.S./Canada
Disaggregation of revenue by major customer markets
Net sales	473.4	408.9
Aviation Services | Europe/Africa
Disaggregation of revenue by major customer markets
Net sales	108.8	91.4
Aviation Services | Asia/South Pacific
Disaggregation of revenue by major customer markets
Net sales	64.0	41.2
Aviation Services | Other
Disaggregation of revenue by major customer markets
Net sales	15.5	8.2
Expeditionary Services
Disaggregation of revenue by major customer markets
Net sales	25.5	19.1
Expeditionary Services | Commercial
Disaggregation of revenue by major customer markets
Net sales	1.3	2.1
Expeditionary Services | Government and defense
Disaggregation of revenue by major customer markets
Net sales	$ 24.2	$ 17.0