The function $f$ is defined by $f(x)=(x+1)(x-3)(x+2)$. In the $xy$-plane, when the graph of the function $f$, where $y=f(x)$, is shifted down 5 units, the resulting graph is defined by the function $g$. If the graph of $y=g(x)$ crosses through the point $(2,b)$, where $b$ is a constant, what is the value of $b$?