$\text{A = 5 + $5^{2}$ + $5^{3}$ +......+ $5^{2017}$}$
$\text{5A = $5^{2}$ + $5^{3}$ +......+ $5^{2017}$ + $5^{2018}$}$
$\text{5A - A = ($5^{2}$ + $5^{3}$ +......+ $5^{2017}$ + $5^{2018}$) }$
$\text{- (5 + $5^{2}$ + $5^{3}$ +......+ $5^{2017}$)}$
$\text{4A = $5^{2018}$ - 5}$
$\text{Theo bài ra, ta có:}$
$\text{4A + 5 = $5^{x}$}$
$\text{⇒ ($5^{2018}$ - 5) + 5 = $5^{x}$}$
$\text{$5^{2018}$ - 5 + 5 = $5^{x}$ }$
$\text{$5^{2018}$ = $5^{x}$ }$
$\text{⇒ x = 2018}$
