The large majority of protoplanetary disks have very compact ($\lesssim 15$AU) continuum emission at mm wavelengths. However, high angular resolution observations that resolve these small disks are still lacking, due to their intrinsically fainter emission compared with large bright disks. In this letter, we present $1.3$mm ALMA data of the faint ($\sim 10$mJy) disk orbiting the TTauri star CX Tau at a resolution of $\sim 40$mas, $\sim 5$AU in diameter. The mm-dust disk is compact, with a 68$\%$ enclosing flux radius of 14$$AU, and the intensity profile exhibits a sharp drop between 10-20$$AU, and a shallow tail between 20-40$$AU. No clear signatures of substructure in the dust continuum are observed, down to the same sensitivity level of the DSHARP large program. However, the angular resolution does not allow to detect substructures at a scale of the disk aspect ratio in the inner regions. The radial intensity profile resembles well the inner regions of more extended disks imaged at the same resolution in DSHARP, but with no rings present in the outer disk. No inner cavity is detected, even though the disk has been classified as a transition disk from the spectral energy distribution in the near infrared. The emission of $\mathrm{<mrow\; data-mjx-texclass="ORD">12</mrow>}$CO is much more extended, with a 68$\%$ enclosing flux radius of 75$$AU. The large difference of the mm dust and gas extents ($>5$) strongly points to the occurrence of radial drift, and matches well the predictions of theoretical models.