Adding new vent fan...can I........??

Hi guys. I have a slight issue with adding a new bathroom fan where there wasn't one before. The bathroom is on an outside wall and the fan will be about 5 feet from the outside wall. There is very little room to work within the attic space and it has a drop ceiling (12" mdf tiles). The tiles cant be rmoved without runing them as they were staples and glued in place. I was wondering if I could vent the duct at the soffit in the attic. Not just ending it at the soffet but actually cutting a square hole in the soffit and adding a wall style duct only having it facing the ground. Sounds stupid I'm sure but if you saw the area and type of ceilng I have to work around, you would understand. I have 14" above the tub window to exit a vent but access to the space over the drop ceiling is difficult. The attic is finished on the floor over the bath. Just trying to do something easy. Was hoping I could get away with NOT going thru the roof. Your thoughts?

Venting into the eave... the area under the soffit.... can lead to dry rot and mold formation, due to the inability of the high moisture to go anywhere!

It doesn't sound like you have a drop ceiling anyways, but I suggest you drop the ceiling and replace it with a more modern on after you've run your rigid duct.

The warm, moist air wants to go up, so doing it in the sofit has problems with condensation as it gets trapped. An end wall, or one designed to go out through the wall, or through the roof has their advantages.