#### Answer

$x=\pm 5i$

#### Work Step by Step

Step 1: $x^{2}+25=0$
Step 2: $x^{2}=-25$
Step 3: Using the square root property, $x=\pm\sqrt {-25}$.
Step 4: $x=\pm\sqrt {-1\times25}$
Step 5: $x=\pm\sqrt {-1}\times\sqrt {25}$
Step 6: $x=\pm i\times5$
Step 7: $x=\pm 5i$