Just did my 2002 530i, driver’s seat recline right side failure.
There are two motors with four cables. The upper one for the headrest and the lower one for the seat recline.
It is an easy fix and worth doing all four cables.
If you don't want to do all four cables it is worth holding the cables while you move the seat to identify the correct cables to fix.
Do not turn the key on with the seat unplugged or you will get an Airbag light.
There should be 15mm of inner cable sticking out once you cut the outer cable and reattach the metal end piece. It is very easy to cut with a box cutter.
I used a soldering iron to heat the metal end fitting, which worked well.
Tightening Torques
Front seat to floor 42 Nm (31 ft-lb)
Seat belt to seat frame 48 Nm (35 ft-lb)