The $\mathbb{C}$-motivic Adams Spectral Sequence for $s\le 5$

We determine the ${\tau }^n$-torsion in the first 5-lines of the $E_2$ page of the $\mathbb{C}$-motivic Adams spectral sequence using the techniques of Burklund-Xu. In particular, every element in this range is either ${\tau }^1$-torsion or $\tau$-free. We also show that ${\tau }^n$-torsion elements can appear only in Adams filtration at least $2n+2$ and give further evidence of a possible $3n$ bound.