Can I use a 5hp vfd on a 2hp or 3hp motor?

[TDKPE]

I suspect it will work, given the clarification.  And a lathe is generally a pretty light load, regardless of motor size, though if you really lay into a big roughing gouge you certainly could put some load on it.  

I've always had 1/3 and 1/2 hp motors on my old 12" lathe and never felt that I needed more, but it's a small lathe and I'm not turning table tops on the outboard side.  I now have a 1 hp 3-phase motor on a VFD, and the only reason I need a large motor is so that when it's running below rated speed it can still maintain the torque needed.*  

If you overdrive the VFD on single-phase power, it will probably just fault out on undervoltage.  If the unit is cheap, I'd give it a go.

*Set to V/Hz mode (volts-to-hertz), the motor will maintain rated torque even as you slow it down (<60 Hz), but power is reduced linearly, so running at half-speed will output half-power (power equals torque times speed).  Using a motor twice as big as you would normally need means you can slow it to half speed without actually losing any capability.  That's why VFD lathes generally have 'oversized' motors.  Running the motor faster than rated speed (>60 Hz) the drive will work in constant-power mode, which means torque will drop off as speed increases.

[Gregory of Sherwood Forest]

Yeah, I want to try and maintain torque at low speed. That's concern #1 for this lathe, used more outboard turning.

[TDKPE]

Gear it as low as it goes, then slow it to where you need with the variable speed. Low gearing keeps the motor torque requirement as low as it will go, and the oversized motor produces adequate torque when running slower than design speed. Even better if you use a 1200 rpm motor, as the inherent torque will be 50% greater than an 1800 rpm motor of the same power rating, and it's already running at 2/3 of the speed of the 1800 rpm motor before dropping the frequency below 60Hz. 1200 rpm motors are not too hard to find, either.

I have a 1/2 hp single-phase motor that I used to use on my lathe, but it still wasn't slow enough for really rough, unbalanced stuff, so I went to a VFD and three-phase motor to get the speed where I was happy with it.

Like this one https://www.ebay.com/itm/Baldor-3-Hp-114...rk:10:pf:0

or this 2 hp motor https://www.ebay.com/itm/NEW-BALDOR-AOM3...rk:26:pf:0

[BloomingtonMike]

The 7300 is a sensorless vector drive so full torque at 1 hz. That is better than 6hz ov v/hz. Id not use v/hz even if it has it. Is the lathes motor inverter rated?