A novel pepper hybrid plant, designated HMX5125 is disclosed. The invention relates to the seeds of pepper hybrid HMX5125, to the plants and plant parts of pepper hybrid HMX5125, and to methods for producing a pepper plant by crossing the pepper hybrid HMX5125 with itself or another pepper plant. The invention further relates to methods for producing a pepper plant containing in its genetic material one or more transgenes and to the transgenic plants produced by that method and to methods for producing other pepper plants derived from the pepper hybrid plant HMX5125.
