Is the X5 lens such that it does not focus on "infinity" Is it broken?
even after calibration, it does not focus on infinity.

Hi, sir. Did you mean X5 camera? Can you post some pictures with the problem so we can locate the problem. Please note that our camera can work in the temperature range from 0℃ to 40℃, it may lose focus if the camera works under -10℃.

Zenmuse X5The temperature is positive. Pictures taken before and after calibration.
AF focus for the rest of the picture

Images do look soft.  Does the same happen with another lens?

Only with X5. Osmo + is fine
Objective Inspire 1v2 also does not have sharp pictures

What happens if you shoot a photo with drone on the ground at a distant object?  That would eliminate any vibration from flight affecting the image.

I have had bad cameras from DJI twice due to tilted sensors where one side was less sharp than the other side, but yours looks soft everywhere.  You may have a bad camera where the bayonet wasn't aligned right from the factory if this is a new camera given your lens works right on the Osmo.

At the AF it is obvious that at some point as the "blades" will catch focus, but the green frame will catch something else - not a sharp image.
The MF graduation gives a sharp image below ∞