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Inequalities can be solved similarly to equations. The only difference is that if we multiply or divide both sides by a **negative number** we have to flip the inequality sign. Here we can solve the inequality by subtracting $5$ from both sides, so the inequality sign remains the same.
$5+x \gt 3 \quad \Leftrightarrow \quad x \gt \text{-}2.$
Thus, the solution set is $x\gt \text{-}2,$ meaning all $x$-values greater than $\text{-}2.$

b

The endpoint $x=\text{-}2$ is not included in the solutions set since the inequality has the symbol $<.$ Therefore, it's marked with an open circle.

Now, the solution set is all $x$-values greater than $\text{-}4.$ That means all $x$-values to the right of the endpoint.