How significant are annular tears at L4 5 and L5 s1? These findings are from MRI after a car accident injury.

Depends. The annulus fibrosus is a thick, fibrous tissue around the edge of the discs in between the vertebrae holding the disc in place. A fissure/tear indicates disruption of some of these fibers. Fissures are very common and most are asymptomatic, but they can be a source of pain, especially if they are close to a nerve. Also, disc herniations may occur through these areas of weakness.
MAYBE BENIGN. Annular tears of the intervertebral discs are very common and may not cause symptoms in the majority of the population. When disc material is extruded through a tear then symptoms of 'pinched nerve' may be present: pain radiating to hip, thigh, lower leg or foot. Also a disc can press on the spinal cord causing 'spinal stenosis' with symptoms of leg weakness and bladder/bowel changes.
Can be painful. Annular tears can be incidental or they can be painful. These are relatively common and are indicative of degeneration of the disc.