4R and 5R transmissions are computer controlled, the engine computer(PCM/ECU/EEC)
55E just means it is for a 4.0l engine, 44E were for 2.3l and 3.0l engines
The computer software is the only difference between 4R and 5R
So there is no benefit in installing a 5R in place of a 4R unless you also change the computer or its software.
5R software turns on OD(overdrive) when RPMs get too high in 1st gear, this gives the 5R its 2nd gear, 4R software doesn't do this.
And that's how the "5th gear" was added to the 5R, 1st + OD = 2nd gear.
4R gears 2.47 /........../1.47 / 1.00 / 0.75 - 4 speed
5R gears 2.47 / 1.87 / 1.47 / 1.00 / 0.75 - 5 speed
When you combine 2.47(1st) with 0.75(OD) you get 1.87, which is the 5R's 2nd gear
This gives the 5R a smoother shift ratio, the 2.47 to 1.47 was quite a gap in ratios
If your 5R is shifting from 1st to 3rd that would be correct using 4R shift control(software), it wouldn't be a DTR issue.
Use the DTR that fits your wiring harness