  In 2017, Andrews, Dixit, Schultz and Yee introduced the function
$\overline{\textrm{spt}}_\omega(n)$, which denotes the number of smallest parts
in the overpartitions of $n$ in which the smallest part is always overlined and
all odd parts are less than twice the smallest part. Recently, Baruah and Begum
established several internal congruences and congruences modulo small powers of
$5$ for $\overline{\textrm{spt}}_\omega(n)$. Moreover, they conjectured a
family of internal congruences modulo any powers of $5$ and two families of
congruences modulo any even powers of $5$. In this paper, we confirm three
families of congruences due to Baruah and Begum.
