Cubic partitions modulo powers of 5

Let p* (n) be the number of partitions of n in which even parts come in two colours (so-called "cubic partitions"). It is known that if alpha >= 2 and delta(alpha) is the reciprocal of 8 modulo 5(alpha) then for n >= 0, p* (5(alpha)n + delta(alpha)) equivalent to 0 (mod 5(left perpendicular alpha/2right perpendicular)). We give a completely elementary proof of this fact.