Answer
See Diagram
Work Step by Step
The problem is made of two distinct sections, which are indicated in the diagram. The first is the acceleration from stop, where the acceleration starts at $5m/s^2$ and all other variables are zero. After 5 seconds, acceleration stops, and velocity has increased to $5m/s^2 \times 5s = 25m/s$.
The second portion of the problem uses the new velocity of $25m/s$ and accelerations at $0m/s^2$ to travel more distance at a constant velocity for 3 more seconds. This brings the total time in the final position to $8s$.
Position is the unknown variable at the middle and final parts of the diagram.
