Lyman-break galaxy (LBG) candidates at z greater than or similar to 10 are rapidly being identified in James Webb Space Telescope (JWST)/NIRCam observations. Due to the (redshifted) break produced by neutral hydrogen absorption of rest-frame UV photons, these sources are expected to drop out in the bluer filters while being well detected in redder filters. However, here we show that dust-enshrouded star-forming galaxies at lower redshifts (z less than or similar to 7) may also mimic the near-infrared (near-IR) colors of z > 10 LBGs, representing potential contaminants in LBG candidate samples. First, we analyze CEERS-DSFG-1, a NIRCam dropout undetected in the F115W and F150W filters but detected at longer wavelengths. Combining the JWST data with (sub)millimeter constraints, including deep NOEMA interferometric observations, we show that this source is a dusty star-forming galaxy (DSFG) at z approximate to 5.1. We also present a tentative 2.6 sigma SCUBA-2 detection at 850 mu m around a recently identified z approximate to 16 LBG candidate in the same field and show that, if the emission is real and associated with this candidate, the available photometry is consistent with a z similar to 5 dusty galaxy with strong nebular emission lines despite its blue near-IR colors. Further observations on this candidate are imperative to mitigate the low confidence of this tentative submillimeter emission and its positional uncertainty. Our analysis shows that robust (sub)millimeter detections of NIRCam dropout galaxies likely imply z similar to 4-6 redshift solutions, where the observed near-IR break would be the result of a strong rest-frame optical Balmer break combined with high dust attenuation and strong nebular line emission, rather than the rest-frame UV Lyman break. This provides evidence that DSFGs may contaminate searches for ultra-high redshift LBG candidates from JWST observations.