The ACOG actually released less restrictive guidelines on vbacs the middle of last year. They now advocate trial VBAC even after a 2nd c/s depending on circumstances and health. However, after having had 4 it is highly unlikely ANY doctor would be willing to forgo the risks to attempt VBAC.
Usually they will only let you attempt a VBAC after having your first c-section. Like LosingMyMind said, you are a great risk for uterine rupture that could kill you and your baby.
If you are referring to a vaginal birth...it's not likely. After having 4 c-sections your risk of uterine rupture has increased significantly. It would really depend on your doctor and how long ago your c/s were.