I am assuming that you want to go across the 5 foot side walk and not the length.
Using 4 inch by 10 foot ABS plastic sewer pipe with notches/teeth cut in the end, I drove approximately 20 feet under the slab of my small barn. I dug a trench about 15 long and 3 feet deep and started the hole by twisting the pipe as I hammered on the outer end with a small sledge hammer. I would pull the pipe out every foot and clean out the dirt. It took me approximately and hour of driving to get 20 feet of the pipe through. There is a lot of sand in my soil so it was not really too difficult. If I did this for approximately 20 feet, 5 feet should be a snap. Another way I go under concrete is to dig a trench on one side of the slab, get a 1/2 inch copper pipe cut to the length of the hole, in your case about 5 feet, take a hack saw and cut one end of the pipe at a sharp angle and solder a brass nut (a number 10 nut should work) inside the pipe at the base of the angle. On the other end of the pipe solder a fitting that can be threaded onto a garden hose. Fasten the hose to the pipe, turn on the water and pressure wash out a hole under your concrete slab where you want the 4 inch pipe to pass.
Good luck.
Farwell