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In this paper we compute the minimal polynomials of Ramanujan values$27t_n^{-12}$ for discriminants D\equiv5mod24. Our method is based on ShimuraReciprocity Law as which was made computationally explicit by A.Gee and P.Stevenhagen. However, since these Ramanujan values are not class invariants, wepresent a modification of the above method which can be applied on modularfunctions that do not necessarily yield class invariants.

Ramanujan Invariants for discriminants congruent to $\mathbf{5\;mod \;24