I would guess there wouldn't be space for the 5th gear in the 4 speed housing? but I'm not sure.
The other option is to convert to cable operated gear change but this is also a lot of work.
Best find a second hand 5 speed box. Although with values of 1300 cars increasing, would you be better off living with 4 speeds to keep it original?
I have just fitted a Tempra 1.6 to my 85 X1/9 but kept the original X1/9 5 speed box.