This article reports the observation of a spontaneous anomalous Hall effect (AHE) in epitaxial thin films of Mn5Si3, a material with a vanishingly small net magnetic moment. The AHE, a signature of time-reversal symmetry breaking, was observed without an external magnetic field. The study demonstrates that the unconventional d-wave alternagnet phase of Mn5Si3 is consistent with the experimental structural and magnetic characterization of the material. Theoretical calculations show that the AHE generated by this phase is sizable and agrees with experimental results. The findings suggest that Mn5Si3 is a candidate for unconventional d-wave alternagnetism, opening new avenues for research and applications in magnetic phases. The AHE is a non-dissipative antisymmetric component of the electrical conductivity tensor, which can arise from certain magnetic orderings. In conventional ferromagnets, the AHE is related to the net internal magnetization. However, in the case of Mn5Si3, the AHE is observed despite a vanishingly small net magnetization, indicating a unique magnetic order. The study identifies this as an unconventional d-wave alternagnet phase, characterized by strong time-reversal symmetry breaking and alternating spin polarization in both real-space and momentum-space structures. The structural characterization of Mn5Si3 shows a hexagonal crystal structure without geometric frustration. The observed AHE is not related to phases stabilized by geometrically frustrated structures, but rather to the d-wave alternagnet phase. Theoretical calculations show that the d-wave spin polarization in the reciprocal momentum space generates a vanishingly small net magnetization and a sizable spontaneous AHE. The AHE is attributed to the unconventional d-wave magnetic order, which is distinct from conventional ferromagnetic or antiferromagnetic phases. The study also compares the AHE in Mn5Si3 with other materials, highlighting the unique properties of the d-wave alternagnet phase. The results suggest that Mn5Si3 could be a promising material for applications in spintronics, valleytronics, and magnetic band-topology. The findings contribute to the understanding of unconventional magnetic phases and their potential applications in technology.This article reports the observation of a spontaneous anomalous Hall effect (AHE) in epitaxial thin films of Mn5Si3, a material with a vanishingly small net magnetic moment. The AHE, a signature of time-reversal symmetry breaking, was observed without an external magnetic field. The study demonstrates that the unconventional d-wave alternagnet phase of Mn5Si3 is consistent with the experimental structural and magnetic characterization of the material. Theoretical calculations show that the AHE generated by this phase is sizable and agrees with experimental results. The findings suggest that Mn5Si3 is a candidate for unconventional d-wave alternagnetism, opening new avenues for research and applications in magnetic phases. The AHE is a non-dissipative antisymmetric component of the electrical conductivity tensor, which can arise from certain magnetic orderings. In conventional ferromagnets, the AHE is related to the net internal magnetization. However, in the case of Mn5Si3, the AHE is observed despite a vanishingly small net magnetization, indicating a unique magnetic order. The study identifies this as an unconventional d-wave alternagnet phase, characterized by strong time-reversal symmetry breaking and alternating spin polarization in both real-space and momentum-space structures. The structural characterization of Mn5Si3 shows a hexagonal crystal structure without geometric frustration. The observed AHE is not related to phases stabilized by geometrically frustrated structures, but rather to the d-wave alternagnet phase. Theoretical calculations show that the d-wave spin polarization in the reciprocal momentum space generates a vanishingly small net magnetization and a sizable spontaneous AHE. The AHE is attributed to the unconventional d-wave magnetic order, which is distinct from conventional ferromagnetic or antiferromagnetic phases. The study also compares the AHE in Mn5Si3 with other materials, highlighting the unique properties of the d-wave alternagnet phase. The results suggest that Mn5Si3 could be a promising material for applications in spintronics, valleytronics, and magnetic band-topology. The findings contribute to the understanding of unconventional magnetic phases and their potential applications in technology.