Answer
$[-2, \infty)$
Refer to the graph below.
Work Step by Step
The conjunction "or" means union.
Recall:
The union of sets $A$ and $B$, denoted by $A\cup B$, is the set that contains the combined elements of $A$ and $B$.
$x\ge-2$ includes all real numbers greater than or equal to $-2$.
In interval notation, the set is $[-2, +\infty).$
$x\ge5$ includes all real numbers greater than or equal to $5$.
In interval notation, the set is $[5, +\infty).$
Thus, the union of the two given sets is $[-2, +\infty) \cup [5, +\infty)$, which when simplified becomes $[-2, \infty)$.
To graph this solution set, plot a solid dot at $-2$ then shade the region to its right.
Refer to the graph above.