In this figure the force should be applied on mass m = 5kg so that it just won't slip is (Given that car is moving with constant acceleration a = 5 m/s² ) and $\mu =0.4$

Suppose I will apply F force on mass m

in vertical direction 

f = mg

μN = mg

0.4×N = 50

N = 125N

In horizontal direction 

 Net force = mass×acceleration

  F−N = ma

F−125 = 25

F = 150N