Low back + distal lt. Leg pain. MRI negative but EMG/NCS says pinched nerves L4-L5 and S1. What can cause this?

Nerve impingement. can be caused by being sandwiched between two spinal bones, pressed by a bulging. It can cause muscle spasm and back pain. Prevention treatment is always recommended. This condition must be professionally managed. See interventional pain management specialist for definitive diagnosis and management. It is the same as a pinched nerve.
Still the spine. Sometimes MRI can be inconclusive but if EMG suggests its the L4, L5 and/or S1 nerve roots, then you have at least an answer that the spine may still be the cause of your back and leg pain. Vice versa, EMGs can also be inconclusive and MRI shows what the pathology is. I would suggest you see a try pain/spine specialist who can best treat you because MRI images may need full evaluation.