  Given an integer partition $(h_1,h_2,\dots,h_k)$ of $n$, is it possible to
find an order $n$ latin square with $k$ disjoint subsquares of orders
$h_1,\dots,h_k$? This question was posed by L.Fuchs and is only partially
solved. Existence has been determined in general when $k\leq 4$, and in this
paper we will complete the case when $k=5$. We also prove some less general
results for partitions with $k=5$.
