  The large majority of protoplanetary disks have very compact
($\lesssim15\,$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 ($\sim10\,$mJy) disk
orbiting the TTauri star CX Tau at a resolution of $\sim40\,$mas, $\sim5\,$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 $^{12}$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.
