We present the properties of two candidate massive (M ⋆ ∼ 1011 M ⊙) and dusty (A v > 2.5 mag) galaxies at z = 5-7 in the first 0.28 deg2 of the COSMOS-Web survey. One object is spectroscopically confirmed at z spec = 5.051, while the other has a robust z phot = 6.7 ± 0.3. Thanks to their extremely red colors (F277W-F444W ∼ 1.7 mag), these galaxies satisfy the nominal color selection for the widely studied “little red dot” (LRD) population with the exception of their spatially resolved morphologies. The morphology of our targets allows us to conclude that their red continuum is dominated by highly obscured stellar emission and not by reddened nuclear activity. Using a variety of spectral energy distribution fitting tools and star formation histories, we estimate the stellar masses to be log ( M ⋆ ) = 11.32 − 0.15 + 0.07 M ⊙ and log ( M ⋆ ) = 11.2 − 0.2 + 0.1 M ⊙ , respectively, with a red continuum emission dominated by a recent episode of star formation. We then compare their number density to the halo mass function to infer stellar baryon fractions of ϵ ⋆ ∼ 0.25 and ϵ ⋆ ∼ 0.5. Both are significantly higher than what is commonly observed in lower-z galaxies or more dust-obscured galaxies at similar redshifts. With very bright ultra-high-z Lyman-Break Galaxies and some non-AGN-dominated LRDs, such “extended” LRDs represent another population that may require very efficient star formation at early times.