The bullet attains the maximum height of 100 m after fired.

If the bullet fired with initial velocity u.

Then, at the height of 100 m, the final velocity of bullet v

From third equation of motion

v² = u²+2gH

g is negative, because the motion is upwards.

0 = u² -2×10×100

So, u = 44.72 m/sec

Now, from the conservation of momentum-

Initial momentum of the system including the gun and the bullet = 0 

Final momentum of the system = momentum of the gun + momentum of the bullet 

                                              = M_gV_g + M_bV_b

                                              = 5×V_g + 5/1000×44.72                      (5 g  = 5/1000 kg)

So, the recoil velocity of gun, V_g = -0.044 m/sec

The negative sign shows that the direction of recoil velocity is opposite of bullet velocity.