Assuming "solution" refers to a real solution (it often does), then yes, he would be correct. However, there are complex solutions for the equation. Let's try to find the solution ourselves to understand the problem better:
[tex]x^2 + 25 = 0[/tex]
[tex]x^2 = -25[/tex]
[tex]x = \pm \sqrt{-25}[/tex]
[tex]x = \pm i \sqrt{25}[/tex]
[tex]x = \pm 5i[/tex]
The solutions of the equation are [tex]\pm 5i[/tex]. The problem is that these solutions are not real solutions, since they involve [tex]i[/tex]. It would often be said that the equation has no solution, even though the equation has complex  solutions.
