Let $X$ be a smooth projective variety of dimension $n$ and $A$ any ample line bundle. Fujita conjectured that the adjoint line bundle $\mathcal{O}(K_X + mA)$ is globally generated for any $m$ greater or equal to $\dim(X) + 1$. One of the standard techniques in the study of Fujita's freeness conjecture is an induction method, called cutting down the minimal log canonical center. In this talk, I will explain how to apply this method to prove Fujita's freeness conjecture in dim 4 and 5.