Gravitationally lensed supernovae (LSNe) are important probes of cosmic expansion, but they remain rare and difficult to find. Current cosmic surveys likely contain 5-10 LSNe in total while next-generation experiments are expected to contain several hundred to a few thousand of these systems. We search for these systems in observed Dark Energy Survey (DES) five year SN fields—10 3 sq. deg. regions of sky imaged in the griz bands approximately every six nights over five years. To perform the search, we utilize the DeepZipper approach: a multi-branch deep learning architecture trained on image-level simulations of LSNe that simultaneously learns spatial and temporal relationships from time series of images. We find that our method obtains an LSN recall of 61.13% and a false-positive rate of 0.02% on the DES SN field data. DeepZipper selected 2245 candidates from a magnitude-limited (m i < 22.5) catalog of 3,459,186 systems. We employ human visual inspection to review systems selected by the network and find three candidate LSNe in the DES SN fields.