I have a 1993 honda accord when I drive for 5 min my car turns off

It is either losing spark or losing fuel.. If there is anyway you can install a spark tester on one of the spark plug wires and let the engine run and see if the spark is still present when the engine stalls out.. Also you may want to install a fuel pressure gauge and watch for a fuel pressure drop when the engine dies. These things are notorious for defective distributors.. I see that you replaced the distributor but just because the part is new or reman then dont just assume that it is working properly. Good luck with your vehicle, this may be a challenge. Chuck