Welcome to TRS
If the explorer also has a 4.0l engine it will work/fit, if not then no
The 4R55E and 5R55E are internally the same transmission with same solenoids, the 5th gear was done by computer software activating OD while still in 1st gear to get a split ratio faux 2nd gear
So the 5R55E will operate as a 4speed same as 4R55E does
There will be 2 extra sensors on the 5R one just above shifter, it doesn't need to be used on a 1995, and one at the rear drivers side for output shaft speed, also not needed in 1995
Your speed info comes from 1995 transfer case VSS sensor
I think you will need to use your 1995 DTR sensor, its on the shifter shaft of trans, not sure if the 2003 will be wired the same, but have a look
If this is your first automatic install one important step to NEVER forget is to install the torque converter inside the bellhousing FIRST, and get it fully seated into the pump and input shaft, spin it and push in, it will slide back farther 2 times as it seats on pump and shaft
Then you can install trans to engine block
Bell housing should go flush to block, NO FORCING them together using bolts, you WILL break the pump and that will be the end of that transmission