Answer
$5t^3-25t^2+115t-575+\frac{{2881}}{{t+5}}$
Work Step by Step
Re-arranging the order of the terms and leaving space for missing terms, the given is equivalent to
$$
(5t^4+0t^3-10t^2+0t+6)÷(t+5)
.$$
Using the long division method shown below, then
$$\begin{aligned}
&
(5t^4-10t^2+6)÷(t+5)
\\&=
5t^3-25t^2+115t-575+\frac{\color{red}{2881}}{\color{blue}{t+5}}
.\end{aligned}
$$
