Sure, let's solve the given inequality step-by-step.
We have the inequality:
[tex]\[ 5 > x + 7 \][/tex]
To isolate [tex]\( x \)[/tex], follow these steps:
1. Subtract 7 from both sides:
[tex]\[ 5 - 7 > x + 7 - 7 \][/tex]
2. Simplify the left side and the right side:
[tex]\[ -2 > x \][/tex]
This inequality can also be written as:
[tex]\[ x < -2 \][/tex]
So, the solution set in interval notation is:
[tex]\[ \{ x \mid x \in \mathbb{R}, x < -2 \} \][/tex]
Thus, the correct solution set from the given options is:
[tex]\[ \{ x \mid x \in \mathbb{R}, x < -2 \} \][/tex]
