Chiral anomaly in quantum field theory is first calculated by Adler, Bell, and Jackiw in 1969. In this paper, 2-dimensional a 4-dimensional chiral anomalies are calculated in several approaches including Fujikawa's path integral method and the direct calculation of the triangle diagram using the dimensional regularization.Then, we discuss the form of the chiral anomaly in 5 dimension. We give the orbifold structures $S^1/\mathbb{Z}_2$ and $S^1/\mathbb{Z}_2×\mathbb{Z}'_2$ to the 5-dimensional space and induce the anomaly term at the orbifold singularities. The 5-dimensional anomaly includes $F\tilde{F}$, the 4-dimensional 'chiral' anomaly. We discuss in detail how this orbifold structures give the anomaly structures in 5-dimensional space.
