Answer
No
Work Step by Step
No, because if $2x+5$ is negative, then $\sqrt{(2x+5)^2}$ will be $-(2x+5)$.
The given equation can be written:
$$|2x+5|=2x+5.$$
For $x\geq -\frac{5}{2}$ the equation becomes:
$$2x+5=2x+5$$
which is true for any $x\geq -\frac{5}{2}$, while for $x<-\frac{5}{2}$ the equation can be written:
$$-2x-5=2x+5$$
which is true only for $x=-\frac{5}{2}$.
Your friend is not correct.
