Can a traumatic knee injury from falling down stairs cause L5-S1 disk herniation and nerve damage?

A knee injury does not usually cause L5-S1 disk herniation.  Likely you injured both the knee and back when you fell down the stairs.     The L5-S1 disk herniation may damage L5 and S1 nerve roots as they exit the spine.  These nerves travel though the pelvis and into the leg and foot to innervate multiple muscles.  L5 nerve root  injury causes weakness walking on your heals, bending your toes to your nose and numbness of the big toe.  S1 nerve root injury causes weakness walking tip toe and numbness in the little toes.    You may need treatment of your back and knee.  Good Luck!