  We show that every bridgeless cubic graph $G$ on $n$ vertices other than the
Petersen graph has a 2-factor with at most $2(n-2)/15$ circuits of length $5$.
An infinite family of graphs attains this bound. We also show that $G$ has a
2-factor with at most $n/5.8\overline{3}$ odd circuits. This improves the
previously known bound of $n/5.41$ [Luko\v{t}ka, M\'a\v{c}ajov\'a, Maz\'ak,
\v{S}koviera: Small snarks with large oddness, arXiv:1212.3641 [cs.DM] ].
