\(A=5+5^2+...+5^{2021}\)
\(A=\left(5+5^2\right)+\left(5^3+5^4\right)+...+\left(5^{2020}+5^{2021}\right)\)
\(A=\left(5+25\right)+5^2\left(5+25\right)+...+5^{2019}\left(5+25\right)\)
\(A=30+5^2\cdot30+...+5^{2019}\cdot30\)
\(A=30\cdot\left(1+5^2+...+5^{2019}\right)\)
Vậy A chia hết cho 30