The difference quotient at 0 lowers each degree by one: a shift matrix

Let $\mathbb{R}_4[t]$ be the vector space of polynomials with degree $\le4$. Find the matrix of the linear operator $L(f(t))=(f(t)-f(0))/t$ with respect to the standard basis $\{1,t,t^2,t^3,t^4\}$.