Vf does not equal 0, it equals -Vi.
The easiest way to look at it is that In free fall the object spends the same amount of time going up as it does going down. Also note that when the object is at the top of its path v=0.
So we know that it is in the air for 3 seconds, therefore at 1.5 seconds it is at its maximum height and v=0.
the change in velovity is 5-0=5 and the accel is 5/1.5 = 3.333m/s^2