It's a Sequence!

$\begin{array} {rccccccccccc} & a_0 && a_1 && a_2 && a_3 && a_4 && \color{#3D99F6} a_5 \\ a_n: & 298 & & 209 && 129 && 58 && -4 && \color{#3D99F6} a_5 \\ \Delta_n = a_n - a_{n+1}: & & 89 & & 80 & & 71 & & 62 & & \color{#3D99F6} \Delta_4 & \\ \Delta^2_n = \Delta_n - \Delta_{n+1}: & & & 9 & & 9 & & 9 & & \color{#3D99F6} 9 & \end{array}$

We note that $\Delta^2_n = 9$ , a constant. Therefore, $\Delta_4 = \Delta_3 - 9 = 62 - 9 = 53$ , but:

$\begin{aligned} \Delta_4 & = a_4 - a_5 \\ 53 & = - 4 - a_5 \\ \implies a_5 & = - 4 - 53 = \boxed{-57} \end{aligned}$