Its quite likely that 'HX5' only identifies the plastic bobbin its wound on. I notice two different wire diameters on the same side of the former, which rules out it being any sort of off-the-shelf isolated pulse transformer, so there is little doubt that it is fully custom wound to the specs of the PSU manufacturer.
Reproducing it would be a PITA for anyone other than the OEM, as it would need to be totally deconstructed to determine exactly how its wound and what (and how many layers of) inter-winding insulation and margining is used, the ferrite characteristics and exact dimensions would need to be identified and matched to a commercially available core, and the thickness of the glue lines in the side and center limbs of the core would need to be measured to determine how its gapped.
An engineer specializing in SMPSU magnetics design with a well equipped workshop would be able to reverse engineer specs for it with a few hours work, but unless you need hundreds or thousands of them, the cost would be prohibitive. Your best bet if you need to source this part for a repair, is to try to source the complete board, even not working, as most SMPSU faults not involving mechanical damage wont damage the transformers.