  The classical spectral Tur\'{a}n problem is to determine the maximum spectral
radius of an $\mathcal{F}$-free graph of order $n.$ Let $\mathcal{K}_{k}^{-}$
be the set of all unbalanced $K_k.$ In this paper, we focus on the spectral
Tur\'{a}n problem of $\mathcal{K}_{k}^{-}$-free unbalanced signed graph for
$k\geq5$. Moreover, we give an answer for $k=5$ and completely characterize the
corresponding extremal signed graph.
