Mobile air conditioner wall duct, anyone done this?

[AliBingo]

We have one of those mobile airconditioner single rather than split units on wheels, it's an Electrolux and it came with a vent fitting and some hose and a plate to fit in a window opening, but I wnat to vent it through the wall.

The trouble is, I don't know what vent to buy which will be compatible - is there some sort of standard size for AC units?

The hard plastic bit that fits on the unit is 6.5" in diameter and the ducting supplied seems to be 6 or 6.5" but the outlet thing at the other end (which I suppose is the bit I'd plug into a wall vent) is more like 5 or 5.5".

Has anyone done this/got any recommendations please?

Thanks!