introduced by Vu [@vu]. A [*strong list edge-coloring*]{} of a graph $G$ is an assignment of lists to $E(G)$ such that a strong edge-coloring can be chosen from the lists at each edge. The minimum $k$ such that a graph $G$ can be strongly list edge-colored using any lists of size at least $k$ on each edge is the [*strong list chromatic index*]{} of $G$, denoted ${\chi_{\ell,s}'(G)}$. Borodin and Ivanova [@BI] asked if there are sparsity conditions that imply ${\chi_{\ell,s}'(G)}\leq 2d-1$ for a planar graph $G$ with maximum degree $d$. We generalize the bounds in Theorem \[thm:bi\] to apply to list coloring.

\[thm:mainlist\] Let $G$ be a subcubic graph.

1.  If $G$ has girth at least $9$ and $\operatorname{mad}(G) < 2 + \frac{2}{23}$, then ${\chi_{\ell,s}'(G)}\leq 5$.

2.  If $G$ is planar and has girth at least $41$, then ${\chi_{\ell,s}'(G)}\leq 5$.

The proofs of Theorems \[thm:sparse\], \[thm:sparse4\], and \[thm:mainlist\] use the discharging method. We begin by proving Theorem \[thm:mainlist\] in Section \[sec:list\] as the proof is shorter and the one reducible configuration is used again in the proof of Theorem \[thm:sparse\] in Section \[sec:sparse\].

Preliminaries and Notation
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Throughout this paper we will only consider simple, finite, undirected graphs. We refer 