A = $5^{1}$ + $5^{2}$ +.....+ $5^{2007}$
=> 5A = $5^{2}$ + $5^{3}$ +.....+ $5^{2008}$
=> 5A - A =( $5^{2}$ + $5^{3}$ +.....+ $5^{2008}$ ) -($5^{1}$ + $5^{2}$ +.....+ $5^{2007}$ )
=> 4A = $5^{2008}$ -5
Ta có : 4A + 5 = $5^{x}$
=> $5^{2008}$ -5 +5 = $5^{x}$
=> $5^{2008}$ = $5^{x}$
=> x =2008