Simplification of a product of four $SU(N)$ structure constants.

Question

I've recently run into the following product of $\mathfrak{su}(N)$ structure constants (defined with skew-Hermitian generators $t^a$, so that $[t^a,t^b]={f^{ab}}_ct^c$): $$ f^{ijk}{f_i}^{ab}{f_j}^{cd}{f_k}^{ef} $$ which has defied all of my attempts at simplification. Can this be rewritten in terms of invariants or smaller products of generators/structure constants? I've only found one reference containing a similar quantity, but it was given in the context of superalgebras. Is there any standard method to reduce larger products of structure constants?