Logarithmic and exponential functions — practice question

Since $(x + 2)$ and $(x + 3)$ are factors of $5x^3 + ax^2 + b$, determine the constants $a$ and $b$.

With these values of $a$ and $b$, factorise $5x^3 + ax^2 + b$ fully, and hence solve the equation $5^{3y+1} + a \times 5^{2y} + b = 0$, giving any solutions correct to 3 significant figures.