Lumbar Radiculopathy (L5 nerve root compression): This is the most likely diagnosis due to the pain distribution from the low back down to the big toe, which is consistent with the dermatomal distribution of the L5 nerve root. Compression of this nerve root can occur due to a herniated disc, spinal stenosis, or spondylolisthesis.

Lumbar Disc Herniation: A herniated disc in the lumbar spine, particularly at L4-L5 or L5-S1, can compress or irritate the adjacent nerve roots, leading to pain radiating down the leg into the foot.
Piriformis Syndrome: The piriformis muscle runs from the base of the spine to the thighbone, and when it compresses or irritates the sciatic nerve, it can cause pain in the buttocks and down the leg, potentially reaching the foot.
Sacroiliitis: Inflammation of the sacroiliac joints can cause pain in the lower back, buttocks, and sometimes radiate down the leg, although it less commonly reaches the toes.

Cauda Equina Syndrome: A serious condition that occurs when the nerves in the spinal canal are compressed, leading to pain, numbness, and weakness in the legs, as well as potential bladder and bowel dysfunction. It requires immediate medical attention.
Spinal Infection (e.g., Abscess or Osteomyelitis): Infections of the spine can cause severe back pain and neurological symptoms, including radiating pain down the legs.
Spinal Tumor: Tumors in the spine can compress nerve roots or the spinal cord, leading to back pain and neurological symptoms such as radiating pain.

Diabetic Amyotrophy: A condition associated with diabetes that can cause severe pain, weakness, and wasting of the muscles in the thighs, sometimes accompanied by back and leg pain.
Arachnoiditis: Inflammation of the membranes surrounding the spinal cord, which can cause severe pain, numbness, and tingling in the legs.
Tarlov Cyst: A type of cyst that can form on the nerve roots in the spine, potentially causing back pain and radiating pain down the legs, although this is less common.