Slip disk @ l5s1, pain in my right upper leg muscles, legs feel weak, shaky & burning pain along outer side, what is wrong?

Nerve irritation. L5-s1 disk herniation (slipped disc) can irritate either the L5 or s1 nerve root. Nerve irritation can cause leg pain, weakness, numbness. The outside of the leg typically means the L5 nerve root is being affected. See your doctor, who can decide if MRI is needed.
L5 radiculopathy. It seems you already got some imaging because you say slipped disc l5-s1--you need examination, then possibly EMG to confirm--you could get epidural injection to help your pain, or go to surgery if there is weakness--- if this is old and you lived with this, rehabilitation.