The invention provides seeds and plants of pepper hybrid SVHH5137 and pepper line HHA-FD16-1393. The invention thus relates to the plants, seeds, plant parts, and tissue cultures of pepper hybrid SVHH5137 and pepper line HHA-FD16-1393 and to methods for producing a pepper plant produced by crossing such plants with themselves or with another plant, such as a pepper plant of another genotype. The invention further relates to seeds and plants produced by such crossing. The invention further relates to plants, seeds, plant parts, and tissue cultures of pepper hybrid pepper hybrid SVHH5137 and pepper line HHA-FD16-1393 comprising introduced beneficial or desirable traits.