1. A curve has the equation

$y={x}^{n}+b{x}^{3}+c$

where $n$ is a positive integer greater than 1, and $b$ and $c$ are integers.

The curve has a $y$-intercept of $-5$.

The curve passes through the point $(1,8)$, at which the gradient of the curve is $45$.

Find the values of $n$, $b$ and $c$.