jmc

Setting $y=0$ in the given functional equation, we get $$f(0)+x=xf(0)+f(x),$$so $f(x)=(1-f(0))x+f(0).$ This tells us that $f(x)$ is a linear function of the form $f(x)=mx+b.$ Since $f(-1)=5,$ $5=-m+b,$ so $b=m+5,$ and $$f(x)=mx+m+5.$$Substituting this into the given functional equation, we get $$mxy+m+5+x=x(my+m+5)+mx+m+5.$$This simplifies to $2mx=-4x.$ For this to hold for all $x,$ we must have $m=-2.$

Then $f(x)=-2x+3.$ In particular, $f(-1001)=\boxed{2005}.$