The invention provides seed and plants of pepper hybrid SV5603PB and the parent lines thereof. The invention thus relates to the plants, seeds and tissue cultures of pepper hybrid SV5603PB and the parent lines thereof, and to methods for producing a pepper plant produced by crossing such plants with themselves or with another pepper plant, such as a plant of another genotype. The invention further relates to seeds and plants produced by such crossing. The invention further relates to parts of such plants, including the fruit and gametes of such plants.