A neighbor sum distinguishing (NSD) total coloring $\varphi$ of $G$ is a proper total coloring such that $\sum _{z\in E_G(u)\cup \{u\}}\varphi (z)\ne \sum _{z\in E_G(v)\cup \{v\}}\varphi (z)$ for each edge $uv\in E(G)$. Pilśniak and Woźniak asserted that each graph with a maximum degree $\mathrm{\Delta }$ admits an NSD total $(\mathrm{\Delta }+3)$-coloring in 2015. In this paper, we prove that the list version of this conjecture holds for any IC-planar graph with $\mathrm{\Delta }\ge 10$ but without five cycles by applying the discharging method, which improves the result of Zhang (NSD list total coloring of IC-planar graphs without five cycles).