Determine the force and its direction on 2kg block in the given situation.It is known that the two blocks move together.Can we determine the coefficient static friction bet the two blocks.If yes then what is its value?

Since the 2 blocks move together, we can consider it as a single system. So, we will get the acceleration of the system:
a= Fnet/Mass = 5/5 = 1m/s2.
Now we need to verify this with the 2kg block. The only source of movement for the 2kg block is the friction. So the friction should provide the necessary acceleration of 1m/s2.
After drawing the FBD for 2kg block, we get the eqn as: f >= 2*1
==> 20 u >= 2.
==> u >= 1.
Note that the greater than sign is used because friction tries to stop relative motion. So, taking a mew value greater than 0.1 will not affect the acceleration since even then, the frictional force acting on the block will be 20N.
Hope this is satisfying.