A bull with a weight of 500kg runs at a speed of 15 m/s and hits at a standing idle 70kg weighing man. After impact, the idle man has thrown at speed of 5 m/s and the bull has slowed down its speed to 10 m/s. What would be the sum of the kinetic energy (in joules) of the bull and man after impact by the bull, assuming that the bull and the man as a system and the collision is not an elastic one?

Hello!
The fact that the collision is not an elastic one means that some kinetic energy turns into other form(s). Therefore the quantity of kinetic energy before and after the collision is different.
Note that after this collision the bull and the man have different speeds, so they don't move as a whole.
For a mass m moving with a speed V, its kinetic energy is (m V^2)/2. So after the collision the bull has kinetic energy (500*10^2)/2 = 25000 (J) and the man has (70*5^2)/2 =875 (J). Their total kinetic energy is 25000 J + 875 J = 25875 J. This is the answer.
Just in case, compute the initial kinetic energy of the system bull+man before the collision. It is (500*15^2)/2 + 0 =56250 (J), so a huge amount of energy was "used" to damage the man (and the bull).