Can pain in back and leg along with foot drop be caused by a small disc protusion l5s1 if conductive nerve study and emg are normal?

Clarification: The peroneal nerve is comprised mainly of l-5 level functions, and your described disc would be at the wrong site, unless of course, a small fragment has lodged near the l-5 lateral recess. Suppose you could have abnormal proximal sciatic nerve function. Was this directly tested? You might have issue with compression at lateral knee. But could be a focal lesion within central nervous system.

Probably not: If the foot drop is related to the disc protrusion, EMG should have been positive. So your condition may be related to something else and you probably need a complete neurological examination to help localize the injury