(i)[4]
Given that $(x + 2)$ and $(x + 3)$ are factors of $5x^{3} + ax^{2} + b$, determine the values of the constants $a$ and $b$.
(ii)[5]
When $a$ and $b$ take these values, factorise $5x^{3} + ax^{2} + b$ completely, and hence solve $5^{3y+1} + a \times 5^{2y} + b = 0$, with any answers correct to $3$ significant figures.