If we assume g=10m/s^2 & negligible friction
The force needed to accelerate that box by 5m/s^2 would be 500N. This is a very basic one.
The confusion came when an force of 250N (the force a 25kg mass/box would experience in a gravitational field) was exerted on the box, I then tought that the 250N would be cancelled out by the Normal force on the surface, thus the only mass would be the 75kg box and the required force to accelerate the box by 5m/s^2 is 375N.
My question is (for the 2nd diagram), should you calculate the force needed to 'push' the box as if there was a 25kg box resting above it or not? My intuition suggests that previous 375N would be the correct answer.