The invention provides seed and plants of lettuce line SV5033LD. The invention thus relates to the plants, seeds, and tissue cultures of lettuce line SV5033LD, and to methods for producing a lettuce plant produced by crossing a plant of lettuce line SV5033LD with itself or with another lettuce plant, such as a plant of another line. The invention further relates to seeds and plants produced by such crossing. The invention further relates to parts of a plant of lettuce line SV5033LD, including the gametes of such plants.