The major veins that develop in the 5th week of embryonic development are the vitelline veins, umbilical veins, and cardinal veins. The cardinal veins initially form the main venous drainage system of the embryo. Additional veins that develop between the 5th and 7th weeks include the subcardinal, sacrocardinal, and supracardinal veins. As development continues, the major veins reorganize and some obliterate, with the supracardinal veins taking over drainage of the body wall and portions of the cardinal veins forming structures like the superior vena cava.