solve for the inequality

To solve the inequality \( x + 5 \leq 13 \), you need to isolate \( x \). Here are the steps:

1. Subtract 5 from both sides of the inequality:
\[
x + 5 - 5 \leq 13 - 5
\]

2. This simplifies to:
\[
x \leq 8
\]

So the solution to the inequality is \( x \leq 8 \).

In interval notation, this solution is expressed as \( (-\infty, 8] \).