No- the 5-window has the Hemi (they call it an 'overhead valve V8' or something like that on the box, but it's an early Chrysler Hemi), and the 5.0. It's the Tudor sedan... 
 
which comes with the flathead engine and the 5.0. Since your 5-window and the Tudor have the same chassis, the flathead from the Tudor will drop right in. 
 
The one from the '48 would fit too, but might need some modification to the engine mounts, and since it has a manual tranny (the Tudor's flathead has an automatic), you'd also need to dig up a clutch pedal. I can't say for sure, but I think the flatheads in the '32 Tudor and '48 Convert have pretty similar speed parts. 
 
Hope this helps!