Evidence is presented for the decay $B_c+rightarrow J/psi 3pi^+2pi^-$ using proton-proton collision data, corresponding to an integrated luminosity of 3fb$^{-1}$, collected with the LHCb detector. A signal yield of $32pm8$ decays is found with a significance of 4.5 standard deviations. The ratio of the branching fraction of the $B_c^+rightarrow J/psi 3pi^+ 2pi^-$ decay to that of the $B_c^+ rightarrow J/psi pi^+$ decay is measured to be $$ frac{Br (B_c^+ rightarrow J/psi 3pi^+2pi^)}{Br (B_c^+ rightarrow J/psi pi^+)} = 1.74pm0.44pm0.24, $$ where the first uncertainty is statistical and the second is systematic.