Welcome aboard Cain. Glad to have you here. Congrats on the new purchase. Hopefully you'll be a paticipant and hang out with us.
First things first. So if its the OEM transmission, it should be a 700r4 K case and being it falls in the year range of 88-92, its one of the better units, so don't give up for an exhange unless you're getting a like transmisison. 88-92 K case 700r4. Next, did you buy the K5 in this condition with trans not working??? I'd ask how the fluid looked but mentioned it was dry??? Did the dipstick smell burnt?? Was a dark color as if the fluid had gotten very hot at some point??? If you bought it this way, did the previous owner say anything about how the transmission acted or how it went out??? Is it possible the previous owner took the pan off it in hopes of repairing the transmission and realized it was toast??? If you bought it this way, the transmission had to be dry for a reason. Fluid does not evaporate of just go away. Can you tell if the TV cable to the Throttle Body is connected??? Lets hope so, or that is your problem and it being disconnected has toasted the tranmission.
If you bought it running and this problem just happened, how did it go down? Just started acting like it went inot netural or was running fine, then afte being parked it wouldn't go anywhere? It would be nice to know as much as possible, and then were to steer you as to what to do or try next.