Why do you need 5 tall?
I find 6 tall fine.
If you want it to fit correctly, just us a 1x4x5 print brick.
This is true, though last time I checked, we didn't have a 1x4x5 print brick.
OP, not sure whether you know this or not, but we have something called JVS which are doors, buttons, levers, and gates that move. All standard JVS doors are 5 height, so you can easily use those, although I don't think we ever had a lego-styled JVS door. But, I would suggest against using these because they are going out of popular use in replacement for the new, default-style snapping doors, which are a lot better. I recommend switching from using out-of-scale 5 height doors to 6, which is closer to (though still not quite) the realistic size.