Spectral Turán problem for ${\mathcal{K}}_5^{-}$-free signed graphs

The classical spectral Turán problem is to determine the maximum spectral radius of an $\mathcal{F}$-free graph of order $n\mathrm{.}$ Let ${\mathcal{K}}_k^{-}$ be the set of all unbalanced $K_k\mathrm{.}$ In this paper, we focus on the spectral Turán problem of ${\mathcal{K}}_k^{-}$-free unbalanced signed graph for $k\ge 5$. Moreover, we give an answer for $k=5$ and completely characterize the corresponding extremal signed graph.