Answer
$(-2, \infty)$
Refer to the graph below.
Work Step by Step
By subtracting $5$ to both sides we get
$$
2x+5\gt 1 \Longrightarrow 2x+5-5\gt 1 -5\Longrightarrow 2x\gt -4
.$$
Now, by dividing both sides by $2$, we have $x\gt -2$.
In terms of intervals, $x\in (-2,\infty)$.
To graph, plot a hole at $x=-2$ then shade the region to its right.
See the figure below.
