So a few things to consider.
1. Single phase 220V is single phase 220V, you do not get 440V out of the contactor.
2. To use a 3 phase (3 pole) contactor for single phase, what is typically done is single phase power comes in on L1 and L2, a jumper wire goes from T2 to L3, the motor is connected to T1 and T3, this assumes there is an overload relay and some will sense a phase loss. Otherwise just use L1 and L2 in, and T1 and T2 out. You still need to change the size of the overload output, and probably need to rewire the whole panel and motor cable to handle the additional current load for single phase and also a larger motor if you go that route.
3. Power in with single phase, you need to trace back power to transformers or any other sub system and use the two legs to power with single phase. Typically there is a single phase transformer for the contactors and to power other controls or sub systems.
4. The current contactors are probably matched to the current motor size and 3 phase use, running a single phase 5 Hp motor through the same contactors will result in almost 3X the current and they will probably fail quickly and the wiring will overload and could catch fire.
5. The overload protection would need to be changed to account for single phase and the increased Hp, so essentially you would need to replace the contactors and the overload protectors. Doable, but requires replacing the contactors and probably adding overload relays on the outputs. An electrician should be able to do this, the contactor and overload relay would need to be sized to the application. You also would need to consider the input current, for 5Hp single phase motor would typically be 50A feed.
6. TENV vs. TEFC, depends on the dust level and size. Either should work acceptably in this range. A TEFC single phase will be a much more common motor, I would look for a farm duty motor which are made for heavier loads and are sealed to decrease dust and moisture from getting into the motor.
7. Most likely there are other control sub-systems that need to be powered, these need to be factored into the rewiring solution.
8. A VFD may be the easiest solution, something like the KBVF-29 is a very simple 3Hp VFD AC drive (no programming) that would replace the motor contactors and overload devices. The motor is directly wired to the output, there is a low voltage for ON/OFF run. You are running at a single speed and the same direction so you do not need any other connections. They are reasonably priced and simple to install. Alternative if you want something more full featured is the KB KBDF-29 or Teco L510-203-H1-U.
The KBVF-29 is the simplest and most cost effective solution in my opinion and keeps the stock motor. The input wiring may need to be upsized to handle the single phase load to the VFD (10AWG for this model). Single phase motors have more pulsations which can show up as surface finish issues in lathes and surface grinders, but unlikely to be an issue in your application. A farm duty single phase 3 Hp should be equivalent HP wise to your current 3 Hp motor, so I do not see a reason to go to 5Hp single phase and it also may stress other parts of the machine that could cause more damaged if mechanically overloaded.
KBVF-29 (9593) AC Drives, Chassis Inverter - KB-Controls.com, Your online Shopping for AC & DC Controls & Drives