The problem of dissecting a square into squares of unequal sizes has been extensively discussed in the recreational mathematics literature (see for example), but the dissection of triangles appears not to have received so much attention; there are however a number of naturally occurring problems in the dissection of triangles into triangles. The problem we considerhere is the dissection of triangles into five similar triangles; the component triangles must be similar to each other, but may or may not be similar to the original triangle.