Answer
The largest mass that block C can have is 39.0 kg.
Work Step by Step
We can use $\mu_s$ to find the maximum possible acceleration of block B.
$F_f = m_B~a$
$m_B~g~\mu_s = m_B~a$
$a = g~\mu_s = (9.80~m/s^2)(0.750)$
$a = 7.35~m/s^2$
We can use a force equation to find the mass of block C when the acceleration of the system is $a = 7.35~m/s^2$.
$\sum F = (m_A + m_B + m_C)~a$
$m_C~g = (m_A + m_B + m_C)~a$
$m_C~(g-a) = (m_A + m_B)~a$
$m_C = \frac{(m_A + m_B)~a}{g-a}$
$m_C = \frac{(8.00~kg + 5.00~kg)(7.35~m/s^2)}{9.80~m/s^2-7.35~m/s^2}$
$m_C = 39.0~kg$
The largest mass that block C can have is 39.0 kg. If block C had a larger mass, the acceleration would be too great for the force of static friction to accelerate block B, and block B would start to slide with respect to block A.
