Answer
$5 \leq L \lt 8$
Work Step by Step
Given that {$a_{n}$} is a decreasing sequence
$ a_{n} \gt a_{n+1} \gt a_{n+2} \gt a_{n+3} \gt ...$ for all $n\geq 1$
{$a_{n}$} is a bounded sequence since all terms lie between 5 and 8.
By the Monotonic sequence theorem, {$a_{n}$} is convergent
{$a_{n}$} has a limit $L$.
Since 8 is an upper bound of {$a_{n}$}, $L$ must be less than 8.
$5 \leq L \lt 8$
