High T${}_c$ superconductivity in superhard diamond-like BC${}_5$

Using density functional theory calculations we show that the recently-synthesized, superhard diamond-like BC${}_5$ is superconducting with a critical temperature of the same order than that of MgB${}_2$. The average electron-phonon coupling is $\lambda =0.89$, the phonon-frequency logarithmic-average is $<\omega {>}_{\log }=67.4$ meV and the isotope coefficients are $\alpha (C)=0.3$ and $\alpha (B)=0.2$. In BC${}_5$, superconductivity is mostly sustained by vibrations of the B atom and its C neighbors.