Let
\(b_{5}(n)\) denote the number of 5-regular partitions of
n. We find the generating functions of
\(b_{5}(An+B)\) for some special pairs of integers (
A,
B). Moreover, we obtain infinite families of congruences for
\(b_{5}(n)\) modulo powers of 5. For example, for any integers
\(k\ge 1\) and
\(n\ge 0\), we prove that
$$\begin{aligned} b_{5}\left( 5^{2k-1}n+\frac{5^{2k}-1}{6}\right) \equiv 0 \quad (\mathrm{mod}\, 5^{k}) \end{aligned}$$
and
$$\begin{aligned} b_{5}\left( 5^{2k}n+\frac{5^{2k}-1}{6}\right) \equiv 0 \quad (\mathrm{mod}\, 5^{k}). \end{aligned}$$