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Based on the fact that some important theories like string and M-theoriespredict spacetime with higher dimensions, so, in this paper, we aim toconstruct a theory of quintic quasitopological gravity in higher dimensions($n\geq5$). This $(n+1)$-dimensional quintic quasitopological gravity can alsolead to the most second-order linearized field equations in the sphericallysymmetric spacetimes. These equations can not be solved exactly and so, weobtain a new class of $(n+1)$-dimensional static solutions with numericmethods. For large values of mass parameter $m$, these solutions yield to blackholes with two horizons in AdS and flat spacetimes. For dS solutions, there aretwo values, $m_{\rm ext}$ and $m_{\rm cri}$, which yield to a black hole withthree horizons for $m_{\rm ext}<m<m_{\rm cri}$. We also calculate thermodynamicquantities for this black hole such as entropy and temperature and check thefirst law of thermodynamics. Finally, we analyze thermal stability of the$(n+1)$-dimensional static black hole at the horizon $r_{+}$. Unlike dSsolutions, AdS ones have thermal stability for each values of $k$, but flatsolutions are stable with just $k=1$.

Thermodynamics of static solutions in (n+1)-dimensional Quintic Quasitopological gravity