Let's start by determining the force applied, since we know that Work = F*d.
We can determine the force applied from Newton's 2nd Law: F=ma. We know the mass, but we don't know the acceleration, so we can use kinematics to determine our acceleration:
vi=2.5 m/s
vf=4 m/s
Δt=5s
a=?
Use vf=vi+at ==> a=(vf-vi)/t = (4m/s - 2.5 m/s)/5s = 0.3 m/s^2
Now we can determine the force applied: F=ma = 5kg*0.3m/s^2 = 1.5 kg*m/s^2 = 1.5 N
Finally, we need the distance over which this force was applied, d. Let's find this by going back to our kinematic equations:
vi=2.5 m/s
vf=4 m/s
a=0.3 m/s^2
Δt=5s
Δx=?
We can get this from vf2=vi2+2aΔx, which, solving for Δx, gives us 16.25m
Now, calculating Work = F*d, we have 1.5 N * 16.25m ˜ 24.4 N*m = 24.4 J