I have the latest firmware in my OSMO with an X3 camera.

  

I have the latest firmware in my Inspire-1 Pro with an X5 camera.

  

I have the latest DJI Go app on all devices.

  

Can I replace the X5 on my Inspire-1 Pro with the X3 off my OSMO without any firmware adjustments?

I would put the SD card out of the X5 into to the X3 after I attach the X3 to the Inspire-1 Pro - right?

Thank you in advance for your comments and help.

The Inspire X3 and the Osmo X3 are different. The mechanics of the Osmo require that the gimbal be flattened and locked. So the Osmo X3 can't be used on the Inspire.

Source: Page 26 of Osmo User manual

However, the Inspire X5 camera can be used with the Osmo after it has been upgraded with the latest firmware. However, you will need an adapter which is still unavailable from DJI. Some have used the 3D printed version from  pattern available HERE., or spent $100 on this Metal adapter ring.