Initially, blocks are at rest. Work done by friction in the first 5s is zero. Work done by $F = 24N$ in the next 5 s is 1800J. How many among $0.05, 0.15, 0.25$ are acceptable values for coefficient of friction?
(Friction exists between m and M only)

During first 5s work done by frictional force is zero, hence the mass m has not slipped over M and obviously it will never slip again. They will move together. 

Given : $\mathrm{m}=5\mathrm{M}$

Let say acceleration of both the blocks is $a$.

$24=\left(M+5M\right)a$

$\Rightarrow a=\frac{4}{M}$

Displacement of top block from t=5s to t=10s is

$S=\frac{1}{2}a\left({t_2}^2-{t_1}^2\right)=\frac{1}{2}\times \frac{4}{M}\times \left({10}^2-5^2\right)=\frac{150}{M}$

Work done by F force on top block is

$$\begin{gathered} 1800=FS \\ \Rightarrow 1800=24\times \frac{150}{M} \\ \Rightarrow M=2kg \end{gathered}$$

For top block, 

$24-f=5Ma$

$\Rightarrow f=24-5Ma=24-20=4$

No slip condition, 

$f\le f_L$

$$\begin{gathered} \Rightarrow 4\le \mu 5Mg \\ \Rightarrow 4\le \mu 100 \\ \Rightarrow \mu \ge 0.04 \end{gathered}$$