You need to know the coefficient of static friction between a wooden object and a wooden surface. I'll denote it with µ. If you're given a specific value you should obviously use that.
By Newton's second law, the horizontal and vertical net forces are
• net horizontal:
∑ F = p - f = 0
• net vertical:
∑ F = n - w = 0
where
p = magnitude of the pushing force
f = mag. of friction
n = mag. of the normal force
w = weight of the crate
The second equation gives
n = w = (5 kg) (9.8 m/s²) = 49 N
Friction is proportional to the normal force by a factor of µ, so
f = µ (49 N) = 49µ N
To overcome static friction, the push has to exceed this in magnitude, so that
p > 49µ N
For instance, if p = 0.25, then p would need to greater than 12.25 N. (This example isn't particularly helpful, though, since both possibly correct options are larger than 12.25 N...)