Goodwill and Other Intangible Assets, Net (Details) $ in Millions	12 Months Ended
May 31, 2024 USD ($)	May 31, 2023 USD ($) segment item
Goodwill
Number of operating segments \| segment		3
Number of reporting units \| item		3
Changes in the carrying amount of goodwill
Goodwill, beginning balance	$ 175.8
Foreign currency translation adjustments	0.5
Goodwill, ending balance	554.8	$ 175.8
Product support business
Changes in the carrying amount of goodwill
Acquisition	375.2
Trax USA Corp
Changes in the carrying amount of goodwill
Acquisition	3.3
Parts Supply
Changes in the carrying amount of goodwill
Goodwill, beginning balance	38.9
Goodwill, ending balance	38.9	38.9
Repair & Engineering
Changes in the carrying amount of goodwill
Goodwill, beginning balance	41.4
Goodwill, ending balance	416.6	41.4
Repair & Engineering \| Product support business
Changes in the carrying amount of goodwill
Acquisition	375.2
Integrated Solutions
Changes in the carrying amount of goodwill
Goodwill, beginning balance	76.7
Foreign currency translation adjustments	0.5
Goodwill, ending balance	80.5	76.7
Integrated Solutions \| Trax USA Corp
Changes in the carrying amount of goodwill
Acquisition	3.3
Expeditionary Services
Changes in the carrying amount of goodwill
Goodwill, beginning balance	18.8
Goodwill, ending balance	$ 18.8	$ 18.8
Aviation Services
Goodwill
Number of operating segments \| segment		2
Changes in the carrying amount of goodwill
Goodwill impairment charges		$ 115.6
Aviation Services \| Parts Supply
Changes in the carrying amount of goodwill
Goodwill impairment charges		38.9
Aviation Services \| Integrated Solutions
Changes in the carrying amount of goodwill
Goodwill impairment charges		$ 76.7
Expeditionary Services
Goodwill
Number of operating segments \| segment		1

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