Given that ( \(x + 2\) ) and ( \(x + 3\) ) are factors of
$$5 x ^ { 3 } + a x ^ { 2 } + b$$
find the values of the constants \(a\) and \(b\).
When \(a\) and \(b\) have these values, factorise
$$5 x ^ { 3 } + a x ^ { 2 } + b$$
completely, and hence solve the equation
$$5 ^ { 3 y + 1 } + a \times 5 ^ { 2 y } + b = 0$$
giving any answers correct to 3 significant figures.