Find the remainder of $(2x^3-7x^2-19x+8)/(x^2-4x+5)$ without using division

We have $f(x)=q(x)g(x)+r(x)$ with $\deg r<\deg g$. Hence $\deg(r)\le 1$. Now the hint: $$f(5)=q(5)g(5)+r(5)\text{ and }f(-1)=q(-1)g(-1)+r(-1).$$

Hint

Find $a,b,c,d$ s.t. $$2x^3-7x^2-19x+8=(ax+b)(x^2-4x-5)+cx+d.$$

You immediately remark that $a=2$. I let you continue.