A = $5^{1}$ + $5^{2}$ + $5^{3}$ + ... + $5^{2020}$
=> 5A = $5^{2}$ + $5^{3}$ + ... + $5^{2018}$
=> 5A - A =($5^{2}$ + $5^{3}$ + ... $5^{2018}$) - ($5^{1}$ + $5^{2}$ + ... + $5^{2017}$)
=> 4A = $5^{2018}$ - 5}$
Ta có : 4A + 5 = $5^{x}$
=> $5^{x}$ = $5^{2018}$ - 5 + 5}$
=> = $5^{x}$ = $5^{2008}$
$\text{=> x =2008}$