How do we determine the actual value of static friction when it is not necessarily at its limiting value?

In the following problem, three blocks of masses 5 kg, 3 kg and 2 kg are placed on a rough horizontal surface, as shown in the figure. The coefficient of friction between each block and the ground is μ = 0.2. A horizontal force of 15 N is applied to the 5 kg block. The question asks for the force exerted by the 3 kg block on the 2 kg block.

My confusion is not about obtaining the numerical answer, but about the method.

We know that static friction satisfies

$
\boxed{|f_s| \le \mu_s N}
$

which means we only know its maximum possible value, not its actual value.

For example, I don't think we can simply assume that the 5 kg block opposed 10 N by static friction (its maximum) and the 3 kg block opposed 5 N, thereby concluding that the contact force between the 3 kg and 2 kg blocks is zero.

My question is: what determines the actual value of static friction in such problems?