Context. Probing the faint end of the number counts at millimeter wavelengths is important in order to identify the origin of the extragalactic background light in this regime. Aided by strong gravitational lensing, ALMA observations toward massive galaxy clusters have opened a window to probe this origin, allowing us to resolve sub-milliJansky dusty star-forming galaxies. Aims. We aim to derive number counts at 1.1 mm down to flux densities fainter than 0.1 mJy based on ALMA observations toward five Hubble Frontier Fields (FF) galaxy clusters, following a statistical approach to correct for lensing effects. Methods. We created a source catalog that includes ALMA 1.1 mm continuum detections around two new FF galaxy clusters, together with the sources previously detected around three FF galaxy clusters, making a total of 29 detected sources down to a 4.5σ significance. ALMA 1.1 mm mosaics used for our source extraction covered the inner ≈2′ × 2′; FF regions, reached rms depths of ≈55 - 71μJy beam-1, and had synthesized beam sizes from ≈0″.5 - 1″.5 (natural weighting). We derived source intrinsic flux densities using public lensing models. We folded the uncertainties in both magnifications and source redshifts into the number counts through Monte Carlo simulations. Results. Using the combination of all cluster fields, we derive cumulative number counts over two orders of magnitude down to ≈0.01 mJy after correction for lensing effects. Cosmic variance estimates are all exceeded by uncertainties in our median combined cumulative counts that come from both our Monte Carlo simulations and Poisson statistics. Our number counts agree at a 1σ level with our previous estimates using ALMA observations of the first three FFs, exhibiting a similar flattening at faint flux densities. They are also consistent to 1σ with most recent ALMA estimates and galaxy evolution models. However, below ≈0.1 mJy, our cumulative number counts are lower by ≈0.4 dex compared to two deep ALMA studies (namely one that probes several blank fields plus one lensed galaxy cluster, and the initial ALMA Spectroscopic Survey in the Hubble Ultra Deep Field, ASPECS-Pilot), while remaining consistent with the ASPECS Large Program (ASPECS-LP) within 1σ. Importantly, the flattening found for our cumulative counts at ≲0.1 mJy also extends further to ≈0.01 mJy, that is, ≈0.4 dex fainter than ASPECS-LP, and remains in agreement with extrapolations of their number counts down to this flux limit. We find a median contribution to the extragalactic background light (EBL) of 14-8+12 Jy deg-2 resolved in our demagnified sources down to ≈0.01 mJy, representing 75 - 86% of Planck-derived extragalactic EBL estimates at 1.1 mm. Conclusions. We estimate cumulative 1.1 mm number counts down to ≈0.01 mJy along the line of sight of five galaxy clusters that benefit from having rich deep multiwavelength data. They bring further support to the flattening of the number counts reported previously by us and ASPECS-LP, which has been interpreted by a recent galaxy evolution model as a measurement of the "knee"of the infrared luminosity function at high redshift. Our estimates of the contribution to the EBL associated with 1.1 mm galaxies in the FFs suggest that we may be resolving most of the EBL at this wavelength down to ≈0.01 mJy.