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Summary of Significant Accounting Policies - Contract Assets, Liabilities and Performance Obligations (Details) - USD ($)
$ in Millions
 3 Months Ended 12 Months Ended
Feb. 28, 2025
Aug. 31, 2024
Nov. 30, 2023
May 31, 2025
May 31, 2024
May 31, 2023
Contract assets and liabilities            
Contract assets - current       $ 140.3 $ 123.2  
Contract assets - non-current       28.4 24.6  
Deferred revenue - current       (40.3) (14.7)  
Deferred revenue on long-term contracts       (6.4) (7.2)  
Net contract assets       122.0 125.9  
Change in contract assets - current       17.1    
Change in contract assets - non-current       3.8    
Change in deferred revenue - current       (25.6)    
Change in deferred revenue on long-term contracts       0.8    
Change in net contract assets       (3.9)    
Change in contract assets       26.6 17.1 $ 13.7
Accounts receivable, less allowances of $10.1 and $14.1, respectively       354.8 287.2  
Changes in deferred revenue            
Deferred revenue at beginning of period   $ (21.9)   (21.9) (32.4)  
Revenue deferred       (321.9) (311.1)  
Revenue recognized       (307.6) (319.9)  
Other       (10.5) 1.7  
Deferred revenue at end of period       (46.7) (21.9) (32.4)
Remaining Performance Obligations            
Remaining performance obligation       $ 537.0    
Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction, Start Date [Axis]: 2026-06-01            
Remaining Performance Obligations            
Remaining performance obligation (as a percent)       75.00%    
Expected timing of satisfaction of remaining performance obligation       1 year    
Revenue, Remaining Performance Obligation, Expected Timing of Satisfaction, Start Date [Axis]: 2027-06-01            
Remaining Performance Obligations            
Remaining performance obligation (as a percent)       20.00%    
Expected timing of satisfaction of remaining performance obligation       1 year    
Termination settlement proposal            
Contract assets and liabilities            
Contract assets with customer $ 13.5          
Termination amount for equipment and other costs $ 1.0          
PBH contracts            
Contract assets and liabilities            
Contract Charges on non-achievement of minimum volume guarantees         $ 1.9 $ 1.7
Commercial power by hour, contract, amount derecognized from remaining loss reserves     $ 2.0      
Air Line Customers | Termination Of Power By The Hour Program            
Contract assets and liabilities            
Termination charge       $ 4.8    
Change in contract assets       7.8    
Change in contract revenue       7.5    
Repair reserves       2.5    
Obligation to purchase the rotable assets       5.5    
Asset purchase obligation of purchase price       18.7    
Accounts receivable, less allowances of $10.1 and $14.1, respectively       29.4    
Contract assets with customer       1.4    
Air Line Customers | Past Due | Termination Of Power By The Hour Program            
Contract assets and liabilities            
Accounts receivable, less allowances of $10.1 and $14.1, respectively       $ 7.5    
U.S. Government Customer | Next Generation Pallet Contract            
Contract assets and liabilities            
Change in contract assets   9.5        
Equipment and inventory expensed   $ 12.7