  We present a slowly rotating generalization of a black hole modeled by a Solv
horizon geometry, in five dimensional General Relativity. A separable ansatz
compatible with Einstein equations is proposed, which is integrated in terms of
hypergeometric and exponential functions. The solution highly simplifies after
requiring to maintain the same asymptotic behaviour as the non-rotating black
hole and to have finite, non-vanishing charges. We compute the charges of the
solution and also comment on its importance for studying the phase space of the
theory in this sector.
