A weird problem with long division algorithm contradicting division algorithm of polynomials

Question

I was going through some precalculus concepts but suddenly I felt something's a bit weird and I am terribly confused . The function $f(x)=x^5-5x+2$ when divided by $5x^4-5$, and if we implement long division algorithm we get quotient as $\frac{x}{5}$ and remainder as $2-4x$. But we know by division algorithm of polynomials, $f(x)=g(x)q(x)+r(x)$, $deg(r(x))<deg(g(x))$ . Also if we basically consider $q(x)$ as $g(x)$ and vice-versa then we have $f(x)=q(x)g(x)+r(x)$ , but then we have,$deg(r(x))<deg(q(x))$. So, we can say, $deg(r(x))<min(deg(g(x),q(x)))$. But then, again, we get a contradiction by getting remainder as $2-4x$ in the example above as $deg(4x-2)\nless deg(\frac{x}{5})$. In fact, $deg(4x-2)=deg(\frac{x}{5})$. How is this possible ? I am not quite getting this...