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The 300 is the small block ford pattern, the same bellhousing pattern was used on the 302 and 351W V8's. I don't know about 5 speed automatics, but I know that people commonly put in the E4OD transmission, which is a 4spd (including overdrive) electronically shifted automatic transmission. It came in the late bronco up to '96 and the explorer up to '98. It was also in other things like the f-series until '98. If you're set on a 5 spd, the M5OD is an easy to find and simple swap, but it's a standard tranny.
There is nowhere to get a new one, either use a used one or buy a rebuilt one.
It will not fit your block. But that's the easy and cheap part. You can probably have an adapter built for a grand or two. And remember, this is the cheap and easy part.
Now comes the hard part. The five speed auto is all computer controlled. If you don't use a computer you'll have a one speed overdrive transmission. It will start in fifth gear and always stay there.
You'll need a complete wiring harness and the engine and vehicle sensors. You'll need quite a bit of programming knowhow because you'll need to modify the software as nobody has a program to control this trans behind a 300. That will need to be invented.
You do NOT want to tackle this project. You could buy a brand new loaded 2017 for far less than this will cost.
I totally get you and I asked that same question 8 months ago. 5 speed auto is not a cost effective solution but you can go 4 speed if you are looking for that highway gear. Dents were not meant to go 80 in a 3 speed. lol I am in the process of putting in a 4r70w and getting a transmission controller to make all the computer stuff work in my dent. I got a Stroker crate engine coming so my needs may be more then yours. But a 4 speed so do what you need. AOD is the option if you want all mechanical but the 4R70w is the updated improvement.
I went to a pickapart to get a trans out of a 2000 mustang v6 and found a builder in ATL that does it pretty cheap out of his house.