Equivalence of the 3/5 and 2/5 5-cycle double cover bounds

Let $G$ be a bridgeless graph, and let a $5$-cycle double cover be a collection ${\cal C}=(E_0,\ldots,E_4)$ of five cycles in which every edge belongs to exactly two cycles. Equivalence conjecture for strengthened 5-cycle double covers. The conjecture asserting that every bridgeless graph admits such a cover with

$$|E_0|\geq \frac{3}{5}|E(G)|$$

is equivalent to the conjecture asserting that every bridgeless graph admits such a cover with

$$|E_0|\geq \frac{2}{5}|E(G)|.$$

The paper says that the $2/5$ formulation is equivalent to the ordinary 5-cycle double cover conjecture and proposes the equivalence with the strengthened formulation. It remains open.