Domain of 5√-x+7

1. Identify the expression inside the square root: -x + 7
2. Set up the inequality to ensure the expression inside the square root is non-negative:
-x + 7 \geq 0
3. Solve the inequality:
-x \geq -7
Multiply by -1, reversing the inequality:
x \leq 7
4. The domain is:
\boxed{(-\infty, 7]}