  The problem of finding necessary and sufficient conditions to decompose a
complete tripartite graph $K_{r,s,t}$ into 5-cycles was first considered by
E.S. Mahmoodian and Maryam Mirzakhani (1995). They stated some necessary
conditions and conjectured that those conditions are also sufficient. Since
then, many cases of the problem have been solved by various authors; however,
the case when the partite sets $r\leq s\leq t$ have odd and distinct sizes
remained open. We show the conjecture is true when $r$, $s$ and $t$ are all
multiples of 5, $t+90 \leq \frac{4rs}{r+s}$, and $t \neq s+10$.
