#### Answer

Converges to $1$

#### Work Step by Step

$a_n = \frac{5^n}{5^n + 1}$
$a_1 = 0.833333$
$a_2 = 0.961538$
$a_3 = 0.992063$
$a_4 = 0.998403$
$a_5 = 0.99968$
$a_6 = 0.999936$
$a_7 = 0.999987$
$a_8 = 0.999997$
$a_9 = 0.999999$
$a_{10} = 1.00000$
The terms of the sequence seems to get closer to $1$ as $n$ increases.