$A=\dfrac{2021^5+7}{2021^5-1}\\ =\dfrac{2021^5-1+8}{2021^5-1}\\ =1+\dfrac{8}{2021^5-1}\\ B=\dfrac{2021^9+5}{2021^9-3}\\ =\dfrac{2021^9-3+8}{2021^9-3}\\ =1+\dfrac{8}{2021^9-3}\\ 2021^9-3>2021^5-1(2021^9=2021^4.2021^5>2.2021^5=2021^5+2021^5>2021^5+3-1)\\ \Rightarrow \dfrac{8}{2021^9-3}<\dfrac{8}{2021^5-1}\\ \Rightarrow B<A$