I saw a similar question asked, but i think this is going to be more specific. does l5 s1 inflammation have the potential to induce cramps in the legs?

Different nerve roots exit near the disc regions throughout the spine. At the L5-S1 level, it is generally the L5 nerve root that is usually affected. Besides a dull ache or sharp pain in lower back at this level, you may also have whats called a radiculopathy or sciatica. Symptoms can include pain in buttocks, legs and/or toes; numbness in foot or toes; and difficulty raising foot or big toe

Yes, there can be many consequences, and cramping in an L-5 distribution muscle would not be unique. See your doctor to make certain and get medication to manage.