The graph of a polynomial function $f$ has x-intercepts at $(-4,0)$, $(1,0)$, and $(5,0)$. Function $g$ is defined by $g(x)=f(x-3)$. The graph of $y=g(x)$ in the $xy$-plane has x-intercepts at $(p,0)$, $(q,0)$, and $(r,0)$, where $p,q$, and $r$ are distinct constants. What is the value of $p+q+r$?