#### Answer

All the integers less than $-5$, excluding $-5$ itself, make both inequalities true.
$(-\infty,-5)$

#### Work Step by Step

$x\lt6$ and $x\lt-5$
The first inequality includes all the numbers that are less than $6$ and the second one includes all the numbers that are less that $-5$.
Since $-5\lt6$, all the integers less than $-5$, excluding $-5$ itself, make both inequalities true.
We can express it in interval form as:
$(-\infty,-5)$