will 235/60-15 fit a '65 barracud ??

With the right offset wheels you can fit them on the back. I had an F60/14 tire that I think was a bit wider than your tire on the back of my 64 (exactly the same body as a 65) & it fit with no problems. Search for posts by me from quite a while back & you'll find pics & info on how they fit my car. I don't think you can get away with that tall of a tire on front. Watch for interference with the wheel at the outer edge of the upper control arm & where the tie rod attaches to the spindle. I also had some problems with the front tires hitting the lower front edge of the wheel opening when I used an E70/14 tire. Went to an E60/14 & all was fine when I used the same wheels as on the back with the addition of a 7/16" (I think) spacer. I wouldn't recommend spacers though. The post I mentioned gives measurements for the F60 tire. The E70 &E60 tires are long gone so I can't give any dimensions for them.