A Population of Red Galaxies with Very Strong Emission Lines at $z > 5$ Revealed by the NIRCam Medium Bands: ''Classic'' LRDs, Dusty Star-Forming Galaxies, and a Missing Population of LRDs

The NIRCam medium-bands have proven to be efficient at identifying Emission Line Galaxies (ELGs) with high equivalent width (EW) H$\alpha$ and [OIII]+H$\beta$ emission lines. In this paper we exploit this efficiency to identify a sample of ELGs at $4.9 \lesssim z \lesssim 8.9$ using medium-band imaging from the CANUCS, Technicolor, and JUMPS surveys. We find that the ELGs exhibit a strong correlation between continuum color and emission line strength, such that galaxies with bluer UV/optical continua have stronger H$\alpha$ and [OIII]+H$\beta$ emission lines. We identify 26 galaxies that are outliers from this relation, which we call the Red Emission line Galaxies (REGs), because of their red continuum color and strong emission lines. We classify the REGs into three categories: 1) ''classic'' Little Red Dots (LRDs) selected with common literature criteria, 2) extended REGs, resolved in F444W and consistent with being Dusty Star Forming Galaxies (DSFGs), and 3) compact REGs, unresolved in F444W but not classified as LRDs. The compact REGs fail common LRD selections for several reasons, including faint continuua, contamination from emission lines (very strong [OIII]+H$\beta$), and UV/optical colors that are flatter than those of LRDs. We conclude that the compact REGs are likely LRDs that ''classic'' selection criteria miss, and are therefore missing from existing samples. Our results suggest that medium-band selection can provide more complete samples of these objects.