Answer
$\left( -\infty,-3 \right]$
Work Step by Step
Solving the inequalities separately, then,
\begin{array}{l}
-x+5\gt6\\
-x\gt1\\
x\lt-1
,\\\\\text{AND}\\\\
1+2x\le-5\\
2x\le-6\\
x\le-3
.\end{array}
Using the conjunction "AND", the solution set is the set common to both inequalities. Hence, in interval notation form, the solution is $
\left( -\infty,-3 \right]
$.