What automatic transmission options are there for a 1990 Ford F350 4x4?

Can the newer Ford 5 speed auto be swapped in?

Pretty sure only the C6 was available in '90, I don't think the E4OD was until 92+ in the 350's, not that you would want it anyways. For a 5 speed your going to need to go manual, ZF5 to be exact, no matter what motor you have I'm sure the bolt patterns on the trannies changed, not to mention computer issues with putting that new of a trans in an old truck. What motor do you have anyway, small blocks, big blocks, and diesel were all a different bell pattern.

Since he has a 1990 diesel, he has a 7.3 IDI, non turbo.
The auto trans options were the C6 and E4OD, it came out in 89...
Manual trans was the ZF-5 speed. A 5 speed from behind a 7.3 IDI or a 94-97 Power Stroke will bolt up. The clutch and flywheel will have to be IDI stuff though.

A '90 will have an E4OD. I believe the transition happened at the same time (88) of the 7.3 and ZF-5

A C6 has no electronics and is an easy swap, but lacks an OD, and it wounds like you want to go in the other (newer) direction anyway,

Sorry, I forgot the title when I was writing the response. My '91 was a C6, so it could be either that or the E4OD. I would go manual.